Hmm, I realize now after typing all of this that you asked for Warbirds vs. Aces High not WWIIOL vs. Aces High. I'll keep this up here, though, as I did go through all the work typing it.
I've played a lot of Aces High and a fair amount of WWIIOL. My quick summary: Aces High is much better for flying.
Many more details are as follows. One thing to keep in mind is that WWIIOL (now perhaps called "Battleground Europe") is a much different game than Aces High.
FLYING
In WWIIOL, the general feel of the aircraft, to me, is similarly realistic to Aces High. I suspect Aces High is a lot more realistic in terms of performance details (roll rate vs. speed, speed vs. alt, etc.) and how well the aircraft performance matches actual flight-test data. (I say this because I know of HiTech from way back in the Air Warrior days, I've seen him post messages about details here and there over this past decade, I know a lot of the math behind modelling flight dynamics, and I feel that he knows a lot about and is careful about lots of details that few other games are likely to get right.)
For virtual-world analogs to and subsititutions for real-world effects (how blackouts are handled, how approaching stall is handled, how view is handled, etc.), Aces High is much better. The real fighters generally lacked stall horns, auto trim, etc. However, in real fighters, pilots get the sense of g's and buffetting, which we (sitting in a chair in front of a computer screen) do not. So, it becomes very important how various real-world effects are translated into the virtual world.
WWIIOL's blackouts are much more abrupt than Aces High, which is annoying but which can be gotten used to. In real life, you can easily feel and control g's without having to look at any gauges, so it is important in simulations to have a stand-in for being able to sense g's (and how close you are to blackout) that is similarly easy to use and don't require taking your attention off a target.
WWIIOL doesn't have any stall horn, like Aces High does. It has buffetting as a warning, but when you are in a fight, the buffetting is very hard to notice, when in fact in a real plane that gives buffet as a warning of stall (like a Marchetti SF-260, for example, which I have flown -- although not all planes give good buffetting warning before stall), it is easy to notice, even in a fight. Thus, a stall horn is a better analog of that effect than screen shake and subtle noise changes.
WWIIOL doesn't have a decent autopilot. Yes, most real WWII planes didn't have autopilots, but if you are going to have an autopilot in the first place, you might as well have one that is decent. It makes it so much easier to look at maps and type messages into the radio.
WWIIOL doesn't have built in voice. You can use Teamspeak, but this requires extra hassle and coordination with others. It's much, much better to have the VOX built into the game.
WWIIOL doesn't have auto combat trim. This isn't that big a deal either way. I use combat trim in AH, but it's not that big a hassle to do without it in WWIIOL.
VIEWING
This is the biggest shortcoming of WWIIOL, and it is a major issue, in my opinion. In most aircraft in WWIIOL, you can't see anything out the back of your plane. True, in some of the real aircraft, you didn't have the ability to look straight back (like in a Hurricane). However, in WWIIOL, your virtual self is rigidly strapped into the seat with no ability to move around. There are huge (much, much larger than AH) blind spots behind the aircraft, with no ability to move your head or twist your torso. Sit in your seat and try to look back without moving your shoulders at all -- that's the view you get in WWIIOL.
Also, in terms of being able to keep track of things outside your aircraft, WWIIOL sucks. It treats every view change (such as going from looking forward and left to looking left) as losing sight of an enemy aircraft and reduces the visibility to the icon you have in sight. This wouldn't be so bad, but the skies are generally quite cloudy in WWIIOL.
The effect of the previous two aspects is that, although I rarely lose sight of an enemy I'm engaging in Aces High (or in simulated dogfights in Fighter Combat USA that I've done), I often lose sight of the enemy I'm on in WWIIOL. Also, it is quite frequent for me to get bounced by someone I never see, even though I'm actively scanning around, including checking my blind spot from time to time.
Basically, in my opinion, the view system in WWIIOL sucks. It could be fixed, but I think they consider it to be more realistic, which I don't. It is only more realistic if (1) you can't move at all in your seat in an aircraft, which isn't how you should strap yourself in and (2) you close your eyes for a second every time you move your eyes while tracking an enemy and have to reacquire the target.
It is very, very hard to see ground vehicles in WWIIOL. It's like in Aces High with no icons. Somewhat more realistic (as there aren't icons in real life), but your eye has a lot better resolution than a computer screen and better ability to pick out motion and color differences compared to what you see on a computer screen.
GUNNERY
Gunnery in WWIIOL seems like the planes spew out a lot more bullets than in Aces High (or more precisely that there is much less space between bullets in a bullet stream than in Aces High -- more like a stream from a fire hose). You can sweep your bullet stream across an enemy and have a much higher chance of hitting in WWIIOL. As a result, head ons seem much easier. People who are good at it can hit you in a forward-quarter shot while you are doing maneuvers that would cause you to be almost impossible to hit from the front in Aces High -- or so it seems to me. It is frustrating to be in your Hurricane I and not be able to evade a front shot from a 109 diving on you when you see it coming far, far in advance, go into a good evasive, and the guy manages to hit you without trouble anyway.
DAMAGE MODEL
The damage model in WWIIOL seems a lot more graded in most ways and more lethal in one way. In Aces High, when you hit, you see it (with bright hit flashes), and it doesn't take all that much before debris comes of the enemy or a wing blows off or something catastrophic happens. In WWIIOL, you don't see flashes (so it's hard to tell if you are hitting), and you can get hit with a fair amount of fire and suffer some amount of degraded performance on your plane, but it will still fly. The one way in which lethality seems higher in WWIIOL is that, if you get a pilot wound, you are usually just dead right then -- and that happens frequently if you get a head-on shot.
GRAPHICS
I like the graphics of WWIIOL. I like it in Aces High, too. The WWIIOL world looks more realistic (it does have nice-looking clouds), but frame rates are probably about 1/3 what they are in Aces High, and it is not uncommon for me to get into areas where my framerate drops to about 1 frame/second for a few seconds as I come within range of more people or within range of a city.
GAME ENVIRONMENT
In WWIIOL, you can't fly what you want, when you want, from where you want, on the mission you want. You get to fly what your rank allows you (the crappiest planes at the start) on missions that are posted. That is in some ways a more realistic environment, but the result is that the air-to-air action in WWIIOL is usually very sparse and dull compared to Aces High. A big fight in WWIIOL probably involves 5-10 aircraft total (unless it's some sort of special occasion). Being able to go bomb ground targets is rare -- there rarely are missions up for level bombing buildings or bridges. Being able to divebomb ground vehicles is more common, but not much of that available for low-ranking guys, either.
A typical mission for me in WWIIOL is to take up a Hurricane I (as a low-ranking pilot, I can get that or a Spit I if Spit I's are avail, which they often are not), fly out to a city that is under attack, mill around for a while trying to find any action, finding a plane or three, getting in a swirling fight during which I sometimes lose sight of the enemy even though I am solidly saddled up on him and would never lose him in Aces High, then lose the kill because he runs to friendly robo-gunner ack (which is very deadly in WWIIOL), or I get bounced by several other enemies I never saw until they were on me (despite my looking around).
For flying, I like the game environment of Aces High better. If I want action, I can get just about any type I want in the Main Arena. If I want realism, I can fly in scenarios or squad nights, both of which are more realistic than WWIIOL.
CONCLUSION
WWIIOL is fun for flying once in a while; but the flying aspect feels totally shallow compared to Aces High (few planes up, small fights, not much action, no good VOX, crappy viewing system). Aces High is a much better place to fly.
I fly Aces High for air combat. I play Battlefield 1942 for instant-action ground-combat fun. I play WWIIOL for more realism of ground combat, and once in a while take a plane up for the hell of it.