Hero is better but by how much is determined by what you do with it.  Class to fighter and go crazy with vets 240 + and you have the best fighter in the game (for US or KM).  Do the same with an elite and you will be marginaly better (in stats) then an elite classed on time with max vet and experts.  Both are very expensive options considering you should have at least 8 pilots for a CV6. 

Dont forget to take into account the ability of the opponant to control their planes better then you and take into account numerical superiority of the planes you are taking on but that is a differnt topic.

I you want to put it into numbers aka True Ability here are some rough stats based upon what I have read and calced:

Hero Classed to fighter till level 120 with max vets and experts has a TA of about 5.6M
Elite classed to fighter till 120 with max vets and experts has a TA of about
5.2M?? (I don't have one to be sure of the exact ability stat in my calcs)

Elite classed on time with max vets and experts has a TA of about 4.9M

There are posts describing the relative merits of classing to Ace vs Sd Leader vs just to fighter and why any particular option is best or not so you can research and find all you need to know.

In summary the best possible fighter is a hero with max vet, expert classed to fighter controled by an experianced player.
2nd best same only with an elite.  In practical terms most players (I think) do not go to such extreams and still do quite well with +12 or +13s classed on time.

A better player will generally win the engagement even if the opponants TA is a bit higher all other things being equal.

Enjoy the Game.

Just add more vets to the elite.  Even a good +12 with a few more vets will do the trick.

It is hard to get a general feel for the approximate difference even by testing, which is why one mainly resorts to figures when asked on this subject.

If you take 2 CV's into a room to battle each other, the majority of the time each player will see a different result. It desyncs nearly all the time. I know my fleet mates and I that do this regularly have given up on the idea.

For instance, loading one full wave of ftrs, at the end of the battle i had 7 ftrs left, my fleetmate had 0. On his screen my fleetmate had 5 left, and I had 0. Pretty hard to test heh?

I would say Hero's would be best for CV's as a seaman

Has anyone know the maximum true ability for the fighter and seaman?

Danita is spot on 'The one area the Hero pilots does have a large advantage is in Restore and Repair.

A CV with a Hero crew has more SD ( if you're not at 900 sd) and repair than an elite crew. A hero crewed CV is less fragile than it would have been as an elite crew.' 

 Hero pilots late classed lvl 120 with max vets give me 900SD with only the 6 ftr pilots on board only! 

compare with elite pilots, heros full set give you the following advantages:

(1) 60% more repair rate. (160 from about 100 per sec)

(2) 5%-10% more fighter stats. (about 5 TA from around 4.5 TA)
you can see that how much difference of 14 from 13?

(3)SD will be capped both if you manage the R slot, BO & last support slot correctly.

(4) heros CVN full set cost you 600 medals

assuming vetting all of them to 200. max vet is below 300, however, unimaginable.

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my opinion:

There can be better use for the heros unless you have all 7 nations BB6/SS6 already.