Whenever I get a new hero and assign him/her to a system, they level up at good pace (in my opinion). However, when I assign hero to a fleet, they gain experience and level up really slow. I recruit two Lv 1 heroes from marketplace and assign them at the same turn, the star system hero is over level 10 while the fleet hero is like lvl 4.

Is it supposed to be like this? Or is my fleet not fighting enough?

Both.  

I'd say the rate of exp gain on admirals vs governors is about what it was on ES1.  Governors always outpaced admirals.  So that makes me think it's intentionally that way. 

Your governors gain per turn and from building improvements.  I bet that if you have a battle for every improvement you built, they'd be equal.  

It really depends on your play style.  If you are playing for supremacy and in perpetual war, you'll have more admirals than governors and they'll be higher level.  If you have a lot of peace in between, your governors will be higher level. 

Not sure if it should be tweaked or not.  I'm happy with how it was in ES1.  Given that heroes have actual ships now, I think having a slower gain on Admirals is probably good for balancing since hero ships can be beasts especially in the early to mid game.