There are a lot of areas where AH clearly surpasses AW, a few areas where AW exceeds AH, and some areas where it's anybody's call.
Being years newer, Aces High sports better graphics and true 3D cockpits. The 3D cockpits are especially nice because they allow players to adjust default head positions to see around obstacles, like real pilots would do.
Aces High sounds are customizable, and there are some wonderful sound packs out there to replace the mediocre default sounds.
Aces High's flight model definitely beats Air Warrior's. It models a number of forces not present in AW -- torque, for instance -- and ballistics are the most realistic of any online flight sim.
Aces High allows different convergence settings, numerous bomb loadouts, various gun packages, fuel tanks, and more. Choices here also clearly affect the handling properties of the individual planes.
On the other hand, AW costs only $10/month vs. $30/month for AH. Is Aces High three times better than AH? That's for you to decide after trying it out for a couple of weeks.
Air Warrior also supports user customizable plane and terrain textures via SAC, a wonderful feature for scenarios.
What we can't judge are the intangibles. Is Aces High more fun than Air Warrior? Again, that's for you to decide after playing it for awhile. Which game has the better community? Again, that's for you to decide. Some have noted that the AH community seems quick to jump on newcomers and generally behaves badly. Frankly, I haven't seen this, and the community here has always been absolutely wonderful to me -- even helping me out when my throttle broke (thanks again Schnell!). Air Warrior obviously has a storied history with a large and active community as well. Which is better? Your call after some time here as well.
Hope that helps.

-- Todd/+Dead/DMF