Comparing Aero Elite vs. Ace Combat is like comparing apples and oranges. Aero Elite is the closest you'll get to a flight sim on any console. While not as meticulous as any top grade PC flight sim, it features a lot more realism than in all the Ace Combat games combined. Training missions in AE may seem mundane, like performing a successful barrel roll, loop, etc., but it does pay off after playing a lot of AC (where flight physics just go out the window). Graphics-wise, Sega's AM2 division did a bang up job with the plane models (I think they were even assisted by the JSDF), but Namco's renditions are just a tad better. However, AE does allow you to pilot helicopters and Harriers, something the AC series has yet to feature.
AC, on the other hand, gives you really pretty planes with a truckload of missles and bombs to blow crap up. You can't go wrong with that (ignore Lethal Skies, Top Gun, etc.).
Anyhoo, they're both fun games, just on different levels.