At the same difficulty level, WC4 is substantially more difficult than either WC3 or WCP. This seems to me to be due to two factors: (1) the AI is probably the best out of any WC game...the computer pilots know about team tactics and tricks to get the most out of their fighter relative to yours, and (2) the AI is far more likely to use missiles, and use them well, and missiles in this game are far deadlier.
To make it easier, I would advise four things:
* Emphasize your own survival higher than maybe you are. If you're close to a kill and someone gets on your tail or launches a missile, FORGET ABOUT THE KILL and do whatever it takes to evade. Don't try to "just finish this one guy off"...you probably will die.
* Get really good at dodging missiles. Don't just span the decoy button...you'll run out too fast. Look at where the missile is coming in from, break across it's path, drop one decoy, and then hit your burners. Then break hard another way, and hit your burners again. If you still haven't shaken it, drop another decoy and repeat. Think about what other craft do when they annoyingly dodge your missiles, and copy that.
* Get to know the craft you're flying and use its strengths. Hellcat: just dogfight, it's a well rounded craft. Longbow: use the lethality of missiles to your advantage and spam a bunch of FF's when swarmed by light fighters. Banshee: get good at roll-yaw, and learn to make that scatter gun or those leech cannons count. Vindicator: DON'T think of it as a medium fighter--it's really not--fly it like a Shrike or light bomber instead. Avenger: No real advice here--it's heavy and well rounded. Bearcat or Lance: just have fun.
* If you're playing the PSX version, don't. Get on e-Bay, buy a PC version, use the tech support forums here to get it running on modern computers, and play it that way. The PSX version is significantly harder to fly and dogfight in, and the controls are far less intuitive (at least to me).