If you're flying smart and sticking to BnZ, there is very little difference between the two. Saxman's got the right of it.
One thing I haven't seen touched on is the difference in power between the -1A and the -1D. One peculiarity of the -1D that I find comes in handy now and then is, the additional power lets you turnfight a bit better in it than the -1A. With full flaps deployed and WEP, the -1D can haul itself around riding the edge of stall a lot better than the -1A or the -1. The -1D benefits more from flaps than any of the other variants. It has been known to cause carpal tunnel from constant use of the flaps raise and lower switches though.
Mind you, IMO if you're turnfighting in an F4U, you've messed up pretty bad to get into that situation. 
If you're keeping the speed up and not into micromanaging the flaps, the -1A is the better choice for air to air. Shiv's right about the -1 as well, there isn't much between them if you can deal with the birdcage view.
Wiley.
Our F4U-1A is a late-block version that uses the exact same engine and paddle prop arrangement as the 1D, so the power of the two is IDENTICAL. The difference is that the 1A has two extra fuel tanks so has more fuel weight at a given % fuel load. However I find this extra weight more a blessing than a curse. The 1A doesn't suffer all that significantly from it, and you also have:
1) A means of balancing the aircraft to help counter torque and her tendency to snap over in a stall (burn LW to 25% and RW to 50%, then go to Main for the duration. This makes the 1A comparatively more stable)
2) A reserve in case your main tank gets hit (which Main Fuel and the Engine seem to always be the first things to go in the Hog)
The rocket tubes on the 1D also add drag (even after you dump your rockets.)
The 1D doesn't have rocket tubes, but zero-point rocket stubs. They do affect top speed, but nowhere near as significantly as actual rocket tubes would.
The one caveat I'll add to what Big Rat says about the Corsair's turn-fighting ability:
Once you commit to a turn fight in the Hog you're there until one of you is spiraling down in flames. She can be very capable in that situation, but once you're in it the Corsair (excluding the -4) doesn't have the level acceleration or sustained climbing ability to get out of it again.