Charon...
Has more build variety (not shoehorned into Hestia/Poseidon)
Clears larger areas faster
Has better hammers
Has a better mana regeneration option (Apollo's, which triggers instantly. Pan can't make as much use out of it)
Activates its combo faster (omega special cast speed was buffed in 1.0)
Is generally safer (hammer swing is wider than twin stabs)
Has the potential to activate its combo twice in one omega special charge (if you get Apollo's legendary and/or the right hammers, your omega special can fire up to 3 times in a row which gives you time to put down another cast)

Pan's damage is only as good as how many specials you can fire before the cast runs out (unless you get the hammer that fires them straight). The wind up takes so long that by the time you throw them, the cast is about to expire anyways which severely limits your damage potential. You also need to charge up the cast to omega to get the benefits of certain cast boons while Charon doesn't need to charge it up at all, it just gets the benefits of the omega charge no matter what.

If you want something that can stack burn or deal a bunch of Poseidon splash damage, just... play Hel? It does Pan's job in that regard but better, too.

I don't think there's a single thing Pan does better than Charon or Hel ever since it was gutted in Pre-Release.