Is Starro's axe magical? Because if it isn't magical, it won't scratch Ares at all. If it is, Starro can probably one-slice Ares' head off like he did to Despero.
Round 2 - Ares w/ Godwave
Having the powers of the Source, a nigh omnipotent being, beyong Lucifer M. and Michael D., is quite formidable. Combine that with Ares' knowledge of martial arts and every form of war tactics kinda gives him a big upper hand over Starro.
Round 3 - Depends. v
If Starro can enslave some meta and super beings, he wins.
If Starro doesn't get any super-powered minions, I'd say Ares because he's a master tactician and knows every single military technique and tactic in the world. Also his necromancy can bring back every dead soldier (ranging from BC to AD) to life to fight for him. If all else fails, Godwave Ares can just wipe out Starro's army himself.