I don't notice any difference between skip and abort level, is there any?

A skip level unlocks the next locked level (this is usually the level after your current level). If you decide to immediately start playing that level, you will auto-abort your current level.

Since aborting levels you are already playing is a big waste of time, you should only use skip level powers to unlock more levels ahead of you if you are either planning on using a multi level power or skipping multiple levels to get to the last level asap.

Skip Level = you open one more map to play after the highest map possible for you.
Abort Level = destroy all your progress, get little AP reward, level not finished, will have to come back and replay it anyway, but with 30% less rewards already. Imho it is best never to abort any sort of level you are playing :D

Abort Level = destroy all your progress, get little AP reward, level not finished, will have to come back and replay it anyway, but with 30% less rewards already.

The AP pool only changes when you complete a level, not if you quit it. Ex: if you play a level worth 500 AP, then quit it to pre-claim 100 AP, the remaining 400 AP is still there when you come back to it.

I hadn't thought of that but you're right ... aborting a level means you take the AP you've already earned, but you reset the progress on it, so still have to finish the entire level, but can only earn the part you haven't already claimed!

So if you're 95% completed a level, aborting a level is a nasty, nasty idea.