Indeed, Luftwaffe was in need of replacing/improving of it's tactical aircraft (Bf 109, Ju 87) as well as strategic aircraft (Bf 110, He 111 and Ju 88). Update of the tactical section went okay - the Bf 109 was supported by Fw 190, Ju 87 was also getting supported/replaced by Fw 190.
I would amend this to say 'Short range tactical' . One of the issues the Germans and Italians faced in North Africa was that both fighters and their best strike aircraft (still the Stuka primarily until Sicily) was a limitation in range. The DAF and etc. had a small advantage here initially but it kept growing.
I'm going to compare ranges here a bit and to compare like to like I'm going to show the manufacturers max range with maximum fuel. These are obviously ball-park.
Axis
The CR 32 is roughly equal to the Gladiator in air combat, but had interceptor range (700 km)
Macchi 200 also had interceptor (600 km) range. Superior to Gladiator but slightly inferior to Hurricane, starts taking heavy losses against P-40 and is being phased out in 1942.
Cr 42 also had interceptor range (800 km) and is inferior to Hurricane. Is used with moderate success as a short range CAS / strike aircraft.
1941 The Bf 109E to G, pretty much all versions, excellent fighter but as we know had essentially interceptor range. (~ 800 km) which means less than half that as as strike radius.
1941 MC 202 was also quite good but had maybe 750 km range.
The Bf 110 had a short range initially (~800 km) but could be extended by drop tanks to a useful 2,000 km. But they were outclassed already when the Hurricanes arrived.
The Ju 87 varied a lot by type, range for the Ju 87B and D could vary from 800 km to 1,500 km but they could only rarely be used beyond the range of fighter escorts.
The Ju 88 had a good range (2,000 km) albeit with a lighter bomb load, and could often outrun Hurricanes, but started taking heavy losses when they encountered P-40s or Spitfires.
The SM 79 had very good range 2,500 km, though less with a torpedo) but was too vulnerable even to Fulmars. The other Italian bombers were even worse for some reason. It was still useful for anti-shipping strikes but took heavy losses.
Late 1942 Fw 190, when it arrived, had a bit better than interceptor range (maybe 1,000 km but considerably less when carrying bombs). Quite effective against Allied fighters initially.
The Do 217 also had a good range (up to 2,000 km) and good speed (an impressive 350 mph / 560 km/h). They were also quite lethal in anti-shipping strikes around Sicily especially with guided munitions, but they also proved too vulnerable without fighter escort and took heavy losses.
Allies
1940 Gloster Gladiators had interceptor range (650 km) and was equal to the Cr 32 in combat. The Lysander was a bit better on range (1,000 km) but both were highly vulnerable to the newer Axis fighters like MC 200 and Bf 110.
1940 Vickers Wellington has excellent range (almost 3,000 km) and are useful initially, but once the Bf 110s are in Theater it's too vulnerable for front line operations, soon relegated to maritime use.
The Swordfish (also 1940) were effecitve in the maritime strike role but only had 800 km range and were vulnerable to MC 200, Bf 110, or even CR 32.
1941 The Blenheim (260 mph, 2,000+ km range) was adequate initially in spite of a small bomb load, but were taking losses to MC 200 and proved hopelessly vulnerable once the Bf 110's arrived.
Late 1941 The early Boston's arrived had very short range and a small bomb loaad but were fast (350 mph max speed) and had good survival rates.
1941 Beaufighters arrived (2,500 km+ range, 330 mph). They have excellent range and prove very effective as maritime strike aircraft and strafers, though vulnerable to Bf 109 and MC 202 in daylight combat, they are more effective than Bf 110 and can strike almost anywhere.
The first modern DAF fighters (1940-41), Hurricanes, also had 'interceptor' range (~950 km, and less with tropical gear). They proved superior to MC 200 and Bf 110 but inferior to Bf 109E and MC 202.
The Maryland had good range (2,000 km) and speed (300 mph) and could strike well beyond enemy lines and into unprotected areas. It began to take the lead on strikes over the Blenheim in spite of an even smaller bomb load.
Late 1941 Tomahawk (1,000 km range) arrived. they had a particularly good drop tank and could hold their own against Bf 109F and MC 202
Early 1942 Kittyhawk types arrived (1,500 km range with drop tank)
Spitfire Mk V (arriving mid 1942) had interceptor range (~800 km) but helped the Allies achieve parity against the Bf 109 and MC 202 on the front lines.
Then by late 1942 and into 1943 the B-25 (2,000 km), the B-26 (4,500+ km), and the B-24 (2,500+ km) started arriving. B-24s are used in the tactical or opertional role like the others.
In early 1943 P-38s (2,000 km on up to 4,000 km range as various improvements were made) and later P-47s (up to 1,200 km, increasing over time) arrived.
Spitfire Mk IX arrived also in early 1943, giving more of an advantage at the shorter ranges.
The Bostons were also improved to the G standard increasing range to 1,500 km, with heavier armament and speed still in the 330 mph range with more guns.
The Albacore also arrived in 1943. It had decent range (1,100 km) and could dive bomb, but was hopelessly vulnerable to Axis fighters.
The net result of this from my perspective is as follows -
1940 - Allied and Axis had parity in fighter quality and both were short ranged. Axis bombers are arguably more effective.
1941 - Axis has superiority but Allies already have a range advantage and can strike beyond the front lines. Axis can use Stukas to very good effect. He 111 can be used though at risk. Axis bombers are conferring a significant battlefield advantage.
1942 - Axis and Allies approaching parity in fighters, but Allies can reach further and strike beyond the front line. Stukas and Ju 88s still being used but taking mounting losses. He 111 is basically relegated to maritime operations. Ju 87 and Ju 88, and even SM 79 are still quite effective in the Maritime role away from Allied land-based fighters. Malta is severely pressured.
late 1942 through early 1943 - Axis and Allies roughly at parity in fighter combat on the front lines. But the Allies can also send escorted strikes deep behind enemy lines, and increasingly effective shorter ranged strikes with large numbers of fighter-bombers (which aren't as accurate as Stukas but are more accurate than most light bombers). Allied strikes are increasingly telling in the ground war. Axis cannot really do longer ranger strikes and Stukas and Ju 88s are taking heavy losses when used in the land war, even when escorted. Axis presses the Bf 109E into service as a fighter bomber, for which it is not really suited (but it's far less vulnerable than a Ju 87). Allies are striking Axis air bases with their light, medium and heavy bombers and destroying large numbers of Allied aircraft, fuel and supplies on the ground, rapidly increasing attrition of Axis aircraft.
later 1943 into early 1944 - Axis and Allies still at parity with fighters in quality but Allied numerical advantage is growing. Allies can basically pick anywhere they want well beyond the front lines. Axis are losing the ground battle - pushed out of North Africa. Sicily and Southern Italy are taken, and Italian fascist government collapses before the Germans can stabilize the lines. The Fw 190 replaces the Stuka and is effective as a fighter bomber but has short range. The Ju 88 soldiers on but taking mounting losses.
It's also worth noting that by 1943 the Allies had better naval fighters available, Seafire, F4F, which reduced the vulnerability of the Air Forces during amphibious and supply operations.
Conversely, the Axis was failing to supply North Africa already by 1942. Axis shipping losses had reached 35% by August 1942. Their attempts to resupply by air with Ju 52 and Me 323 etc. were famously catastrophic failures. The lack of effective long range fighters, and the availability of both longer ranged fighters and long range bombers and strike aircraft by the Allies was key here
On the Eastern Front it's a different situation. Almost all the Soviet fighters are short ranged and have limited altitude capability. The Axis can still use their Stukas albeit with some losses. The Soviets are still struggling to achieve parity in fighter combat at the front lines in 1943 and are taking heavy losses of their short range ground attack planes (mainly Il-2) and bombers (best being Pe-2) but are starting to stiffen up. Axis can do longer-ranged strikes with Ju 88 and He 111 without escorts. Soviets are only doing longer ranged strikes at night by this point. Ultimately the Soviets win Stalingrad and save Leningrad and Moscow on the strength of their ground forces and start pushing the Germans back largely through sheer numbers and gradually improving ground kit.
The Med was critical though, IMO. The Germans started with their air force being a major asset that helped them win battles in 1941. Stukas blow holes in Allied lines.
By the end of 1942 the situation is reversed, the Allies win arguably their first major ground battle (second El Alamein) largely because of longer ranged bombers being able to operate with acceptable rates of losses (with fighter escort) and helping to smash Axis air units on the ground, and Allied fighter bombers and strafers are taking a significant toll on Axis ground forces. It's still in play through early 1943 but then the Axis forces start to collapse in the MTO and they lose vast numbers of men and materiel, ground soldiers and flight crews. More than they can afford to lose.
Strategic part was sorely lacking, there was nothing new to replace the Bf 110, He 177 was flawed, and Ju 288 went nowhere. Only the Do 217 project materialized.
A no-nonsense fast bomber never happened.
Not funny when the enemy has you outnumbered and, very soon, out-performed.
Rather than just strategic / tactical I'd distinguish three types of strikes: Strategic, operational and tactical. Strategic is production and large scale logistics. Operational is local or regional logistics, airfields, supplies. Tactical is front line military and logistic targets.
Axis had the advantage in tactical and operational initially. They lost their operational strike capability fairly quickly.
Allies eventually owned the Strategic air war but not (arguably) until past the turning point in the war (by early 1944 I'd say, though they had certainly forced the Germans to shift a lot of assets to air defense already in the second half of 1943).
When that point actually existed?
Well one key point was Malta. Operation Pedestal (in August 42) was a very close run thing. It came down to one crippled supply ship - the Ohio, limping into port. If the Axis had better bombers available and managed to completely wipe out Pedestal, IMO they could have taken Malta. That would have made life a lot more difficult for the Allies in north Africa. The Axis failure here allowed the Allies to achieve victory a few weeks later at Second El Alamein.
Other key points happened earlier in 1942, and would include the second battle of Tobruk and Mersa Martruh (Axis victories which could have been further exploited except for the ongoing problem of Malta) on to the First battle of El Alamein (mid 1942). This was exactly at the turning point in the Air War in North Africa.
In this battle the Allies had a 3-1 numerical advantage in planes and 2-1 in tanks. Axis strike aircraft were helpful to their armored thrusts but were no longer as decisive as they had been, and were taking heavy losses. Allied light bombers and fighter bombers were arguably more telling and helped tip the scale toward the Allied side, and medium and heavy bombers (already USAAF units were available) were hitting the Axis supplies as far back as Benghazi (900 km away).
It ended up a stalemate but it was close. If the Axis had smashed the Allies they could have arguably taken Egypt. If they had longer ranged fighters which could better contend with long ranged Allied strikes, if they had say, Fw 190s intead of Stukas (which could survive strikes at a better rate), and some kind of effective longer range strike aircraft that could hit the Allied
operational targets, I think they would have won the battle.