TL;DR fighter planes are awersome
I've always been one of those players that is reasonable on foot, average in a tank, but excelling somewhere in the sky (I actually sucked in the planes but the helicopters were my bag in bf4), so I was really nervous about flying in this one.
I spent all my time getting medic, support, scout and assault to 10, then worked on the tanker a little and am now around tank 4-5 before even getting in a plane. I was apprehensive about it because I didn't 'get' the jet; too much lock-on and spam and I just couldn't cope.
I was wrong to wait. I'm not a bomber though, too slow and cumbersome although still pretty devastating, it doesn't fit with my play style. Attack plane? Yeah, I loved it. Loved the combat but found fighters difficult to out turn and relied on switching to tail gunner to take them out (I'll add at this point that I agree with dude on almost all his points about the tail gun, it's just gone a little too far). I used the standard lmg>bombs>flare version mostly although found the tank hunter fun, but less effective than if I was on foot so a bit of a waste.
However the single seat fighter planes are definitely where I excel. If the enemy is constantly spawning planes I will definitely go with the bomber destroyer variant. Noticed iRawr also mention this variant, and I feel almost unkillable in it, and the speed boost means you can get away from most other attack planes on your tail (which is a godsend since no tail gun).
The rockets pack a serious punch and have learnt that it's better to keep off the back of bombers and come in from its sides where it's vulnerable. If you get good hits on your rockets (which are tricky to use but rewarding when you get it right), you can sometimes finish them off in the one run with your gun for an easy triple.
Against attack planes, I'll test the water to check for a tail gunner, if not, I'll get in close, REAL close, and let rip. They're very dead shortly after that. Against good pilots and gunners it becomes more of a challenge but with the greater weaponry, superior agility and a speed boost on top of that to get away in a hurry and they tend not to last more than one or two runs from different angles.
The only real threat is another attack plane of the same variant, but so far I've always managed to get away in this plane either by finding friendly AA or various fancy flying to make them crash or make a mistake so I can get out of their sight line and away from them. I have been shot down and I have made mistakes while learning the nuances so I'm not infallible but if I'm boots on the ground and I get bombed EVER then I'm coming up there to get my revenge.
Other than that, when the enemy are sick of being shot down it usually turns into an AA spam-fest and it can get boring when there's nothing to shoot down, especially taking into account that you have other teammates also looking to shoot down enemy planes as well, it can get boring in the plane as it's not so effective on infantry.
Also... for people that bail out of planes, please don't. It sucks, and I'm going to try and ram you. I've found this following tactic to work well against any pilot who doesn't use first person to look behind: taking a chunk of health off with the gun (50% will do, we don't want to do too much damage) before allowing them to think they have lost you (it's better to get behind in underneath in case a pilot does look behind).
Most pilots will fly crazy for a bit waiting to take damage, do NOT take the opportunity yet. Allow the pilot the false sense of relief as he will then take the opportunity to try and repair while flying straight or on a fixed curve - get in there close and unload all rockets right on his/her tail for an instant kill.