So do choco only level up if you get EXP ?

[Ri_ri]

So long as you would normally get exp, your chocobo will also get exp, so this includes grinding mobs at lvl 50.

However, lower levels do have an advantage 50s do not, where you can build exp chains (they effect the chocobo), and can target mobs higher lvl than you.

But it takes double, if not more, the time to kill them. I remember struggling to kill things in the Sylphlands as 47 SMN, while as 50 BLM, I don't even do my full rotation and they're dead. The level 50 weapons makes a huge difference.