I kind of thought I was a little of a Rocky movie expert. The end of Rocky 3, Apollo says to Rocky, "remember, you fight great, but I'm a great fighter". I still don't know what that means.

It looks like a double edged compliment.
Somewhere along the lines of;
"You're good. But, I'm better."

Was it because Apollo was heavy weight champ for a while?

Something a boxer would say.

Yes, most likely because Apollo was a
more experienced fighter.


Have you ever wanted to compliment someone,
And started the compliment with,
"Don't let this go to your head, but... "


It's sort of like that.
Apollo was letting Rocky know,
not to let it go to his head.

I can see that.

If you set aside the ego of Apollo Creed and treat the statement as a general statement;
It has to do with the professionalism in the art of fighting, which makes Creed's proclaimation false. Rocky did fight great but Creed also fought great. Neither were great fighters because 'great fighter' implies the ability to fight great no matter the discipline.
A truly great fighter would have skill fighting in multiple disciplines, from boxing to MMA to Wrestling. Since neither Rocky nor Apollo were muti-disciplined fighters, neither would be considered to be great fighters.

Tom. You are no fun.

I'm thinking that Rocky had the potential to be a great boxer, but he didn't get there yet. Rocky 3 and 4.