Which one is better?

Most would say Robin.

Billy is a quick-based crit servant while Robin is a nuke. Neither of them does great damage normally, but Billy has one of the strongest crit damage buffs in the game and Robin has one of the hardest-hitting NPs in the game.

Robin's NP needs poison to work properly, so if his first skill's cooldown is high then he is less reliable. That said, if you are willing to invest in him he provides a great return, especially earlier in the game with how ridiculously huge his NP damage is.

I'll be quick about this since I'm tired.
They do two different things Billy is a crit servant that hits hard with his NP, but is more based with his 120% crit damage to enemies.
Robin is simply a tactical nuke meant to kill bosses with his NPs overcharge effect and is weak overall other than that
It's based on what you need though for your questions sake I'll say Robin is better generally if you just want an Archer.

Robin if you're arts team heavy.
Billy if you're quick team heavy.

Robin needs his NP up every now and then to be optimal.
Billy needs crit stars generated for him to be optimal.

Robin nukes bosses with his NP but has a lower NP gain rate.
Billy can't nuke bosses with his NP but has a higher NP gain rate.

Both have an evade skill.
Both have an "NP gain" related mechanic.

Different Servants for different roles.

Robin's probably better for more situations (helping charge NP gauges for other Servants, boss battles, farming high-HP mobs, etc), but Billy's probably more consistently good with a Quick team.

Robin. Billy is difficult to use without a star generator and needs leveling his skills.