There's no one thing I can point to and say "That there, that's why I don't like this game." It's more a conflagration of little things that constantly suck all the fun out of the game for me. Please note that while it will probably read like it, I don't consider the following statements of fact. They are opinions and I am well aware that many will disagree. Anyway, onwards with the complaining.
I think the addition of the rock/paper/scissors melee dynamic is the worst offender. It just takes me out of the game every time I'm forced to use it. I mean, blocking the attack of a leaping alien with my rifle then knocking it over as a marine puts a real dent in the feeling of menace the aliens should convey. Why should I be afraid of something I can stop from hurting me then swat away? If I attempt to avoid using this move I spend the entire campaign walking forwards, then running backwards then walking back to where I was and that is just irritating. The Predator is a little more credible pulling that move off, but it still lessens the impact of the Alien threat.
It hurts the other races too, but in the opposite way. Every time an alien blocked my wrist blades, which on the highest difficulty setting happened a lot, I was mentally yelling "Come on! What the hell?" at the screen. It should just shear right through their arm into their face.
It makes melee as both the Alien and Predator less visceral and brutal and much more obviously a game mechanic. One I do not care for. I gave up on the Predator campaign at the point where I was trying to fight four or five Aliens and they were blocking every light attack, forcing me to either play blocksies with them and hope I'm not shredded as I kill the one I've knocked over or try to time the completion of a heavy attack with a rush forward so it actually lands on something. The block mechanic just makes melee combat much less fun for me. I liked it better the old way. If you let something get close to you as a Marine, you got ripped apart. If you got close to something with the Alien/Predator you ripped it apart.
Why didn't I just blast those Aliens that made me quit with the plasma caster you ask? Because it has to be recharged after two or three charged shots, that's why. The plasma caster got a pretty roughly treated in the PC AvP 2 (it was all but useless in multiplayer on the Alien players) and at first I was pleased to see that it now functioned much better. That feeling didn't last. As soon as I found out how quickly it is depleted I realised it was still pretty useless. I couldn't even get one whole Alien encounter out of it.
Which brings me to the other weapon I didn't like. The Pulse Rifle. The single most iconic weapon of the franchise. Oh the treatment it gets. I have hit aliens with a direct grenade launcher hit only for them to keep coming at me. Not to mention how weak it is as a pure assault rifle. I can kind of see how they might have come to 'balance' the pulse rifle this way as it holds 99 rounds, which is very high for a FPS rifle and it has no real muzzle climb or recoil, however that does not alter the fact that it takes all day to kill anything with it. It just feels weak and weak weaponry is not fun.
The sentry guns bothered me too. Why can I not wreck them? Why do I have to smash the control console behind them? The first time I saw one I emptied my plasma caster at it to no effect before I used the nearby ledge to get around it. Why can't the Alien leap attack them too? It seems stupid that all you have to do to get past them it climb up to the roof. They would be more of a threat if you had to work your way from cover to cover in the walls and ceiling to get into jump attack range.
Also, Tequila was irritating as hell. Putting aside what I consider an extremely poor choice for her name, why does she have to constantly berate me when I don't go from mission point to mission point without stopping to explore? I'm looking for audio diaries and ammo god dammit, shut up! I couldn't even keep moving while listening to the ones I found because she would inevitably butt in with a completely pointless "Hurry up Rookie" line and cut off the recording.
Playing the alien was always my least favourite part of the AvP games so I won't talk much about that except just say that it was less fun and harder to control than it was in both of the earlier PC games.
It's not a terrible game. It looks good and it has some fun moments but for me it is just constantly dragged down by these little issues and missteps in the feel and tone of it until I didn't want to play it any more. I will go back to it eventually, if only to grind through so some of the locked achievements stop laughing at me from my gamer card and hopefully I'll be able to get over all the things getting in the way of my fun, but I'm not optimistic.
I haven't played it in about a week (Heavy Rain came out and Mass Effect 2 drew me back in.) so I am probably forgetting things but I hope that helped a little anyway.