The Typhoon was actually designed and built as a high altitude bomber destroyer, not a low level attack aircraft. The original specification (F.18/37) that it was built to called for an advanced fighter to replace the Spitfire and Hurricane, capable of 400mph+ at 15,000 feet, armed with not less than 12 Bownings and to act as a steady firing platfor for the armament. It just so happened that the Napier Sabre engine performed poorly above about 20,000 feet and the thick wing of the Typhoon gave relatively poor lift and climb at high altitudes. The British eventually realised that it worked well as a low level fighter and so they tasked it with intercepting and chasing th e 'tip and run' jabo attacks that plauged England from mid 1942 through to 1943.
Comparing a Typhoon Ib with a P-47D-27;
Typhoon Ibs came in a couple of different versions depending on the production run, but I'll take the standard Sabre IIa engined version from the fifth production batch (the largest) with the bubble top canopy, whip type aerial and 4 bladed propellor as an equal counterpart to the P-47D-27 with paddle bladded Hamilton prop. Earlier Sabre II variants were a little slower (by 7-10 mph) while later Sabre IIb and Sabe IIc variants were anywhere from 5-15 mph faster at the same altitudes. A Sabre IIa engined Typhoon is probably the most representative version for mid 1944.
The Jug was credited with 3,785 A to A kills during the war, while the Typhoon was credited with just 249. So, in absoulte terms the P-7 was FAR more effective as a combat aircraft. The P-47 also had the lowest loss rate of any single engined fighter in Europe, just .07% of combat sorties flown by a P-47 resulted in a loss, so it wins there. But there were also some 15,600 P-47s built, compared with 3,300 Typhoons.
At sea level to about 8-10,000 feet the Typhoon has a speed and climb advantage, even when you consider the effect of the new props on the P-47. The P-47D-27 pulls about 365 mph at 8,000 feet. The Typhoon Ib does about 385 mph at the same height, variants with a Sabre IIb did about 7 mph more. Above this though, the Sabre has to change stages and drops about 5-10 mph to about 12,000 feet. Here the P-47 has a significant advantage in raw speed (up to 15 mph) and power due to the turbosupercharging, with no loss of power at this altitude.
Between 12000 and 18,000 feet the two planes are roughly equal in terms of speed, generally within 5 mph of each other. The Typhoon tops out at about 405 mph at 18,000 feet, for a Sabre II engined variant. Sabre IIa/b version with a 4 bladed prop did about 412mph at similar heights. At 18,000 feet a P-47 does about 400 mph.
In the rolling plane the P-47 is far superior to the Typhoon, at all speeds. The Typhoon was one of the slowest rolling planes of the war. So the P-47 can change direction more easily, a large advantage in combat.
Turn performance favours the Typhoon, but only just. The RAF rated the Typhoon as slightly inferior to a P-51 in terms of turn, and slightly better than the 190 and Tempest at 10,000 feet. I'm inferring from this that the Typhoon had better turn performance than the P-47, which was judged slightly worse than the Tempset.
Zoom climb favours the heavier and cleaner P-47, as would the dive, although the Typhoon was certainly no slouch there. The Typhoon was rated to over 500 mph in a dive. The notorious tail shedding was a result of sympathetic vibrations and mass balance deficiencies, not to any structural weakness.
Armament wise I feel that the 4 x 20mms were superior to the 8 x .50 cals of the P-47D against a variety of targets (fighter, bomber, ground), but that argument is probably never going to get settled. Its a basic question of rate of fire vs damage per round. Both were VERY efficient against fighter sized targets though. Both aircraft were noted for being exceptional gun platforms, steady at speed and with high rates of fire.
Above 18,000 feet the P-47 was clearly the superior fighter. The problems that the Sabre had at altitude and the turbosupercharging of the P-47 mean that anywhere above this the P-47 simply outclimbs and outruns the Typhoon. In between 8 and 18,000 feet its something of a toss up, the slight superiority of the Typhoon in turn and speed being negated by the better roll, dive and zoom of the P-47. On the deck up to about 8,000 feet the Typhoon has a very slight edge, the Sabre enjoying the heavier air and the thick wing section of the Typhoon providing better lift and climb.
As an all around weapon the P-47 is the better plane; faster at medium to high altitude, with a tougher engine, better warload and much better range. As a low altitude interceptor and fighter-bomber the Typhoon holds some of the cards, and with pilots of equal skill it probably comes off slightly better at below about 10,000 feet. Personally my favourite aircraft of the war is the Typhoon, but as an all around weapon of war the P-47D was much superior.