Well, I don't agree we won all the battles, especially those where the North Vietnamese / Viet Cong were making extensive use of caves and underground tunnels. But if we want to debate Vietnam we definitely have to start another thread for that, it's way beyond the scope of this one.
My point however is that when it comes to the AIR WAR in Vietnam, and I would also say the Korean War as well, the most effective 'bombers' in terms of causing damage to the enemy, were not the ones carrying the most tonnage. B-29s in the Korean War carried a lot of bombs for their day, and B-52s carried a huge bomb load no doubt about it, the F-105 was no slouch either, but were they the most effective weapons of War on the Allied side? I think the tendency to look at the amount of tonnage dropped, and the massive amounts of earth moved along the Ho Chi Minh trail and so on, led to a false sense of accomplishment in Vietnam, and more broadly both during WW2 and in subsequent Cold War engagements. The Corsair, B-26, and F-9F were probably more conducive to winning battles than the B-29 in Korea, and the A-1 Skyraider was probably more useful than the B-52 in Vietnam.
Tactical bombers like the A-4 Skyhawk and the A-37, light aircraft like the OV-1 and OV-10, and of course the various helicopters may have actually mattered more in terms of successes (battles won) during the war.
In WW2, I'd say clearly the most important Allied bomber in the Pacific Theater was the SBD, as it won the battles which turned the tide of the war. Fighter bombers and other tactical aircraft like the TBF / TBM, the SB2C (as troubled as it was) and the various army bombers like the A-20, B-26 and B-25 also played important roles... the B-29 was obviously a devastating Strategic weapon but would it have ever managed to get in range without the tactical successes? B-17 and B-24 were used a lot but didn't seem that great at sinking ships or even destroying island bases for the most part. B-17 and particularly B-24 were good as an ASW / maritime patrol / recon aircraft but that is stretching the definition of 'bomber' a bit.
In the MTO I would say fighter-bombers and US light and medium designs such as the A-20 / DB-7, Martin 167 and 187, B-25, and A-36 dive bomber all played the most important roles. The B-24 was in the mix for sure and did some damage, as was the B-17, but I would not say they were decisive. The single most important bomber type I would say was the Martin 187 Baltimore in British use. The Wellington was also pretty important for longer ranged strikes.
The one area where the heavy bombers were arguably decisive was in NW Europe, but not until fairly late in the war. Arguably already past the tipping point. And it's also arguable how much of a difference they really made to the overall war effort. We know from post-war analysis the most telling Strategic raids were against oil infrastructure, but those were a relatively small number. Perhaps strikes on heavy water plants may have saved the day too, though it's debatable how far along German nuclear scientists actually were.
On the Russian front no US or British bomber types really made a difference. They used several but they were all basically relegated to second or third tier, the important bombers were the Il-2 and the Pe 2, later augmented by the Tu-2.
The battle of the Atlantic was won by Short Sunderlands, B-24s, and a motley assortment of other aircraft, but again mostly in the ASW role. The Swordfish for all it's antiquated features was clearly important in the early war.
