Is skyward spine worse than white tassel in Lohen?

I just got him but I literally have no weapon for him, even white tassel (trashed them all way back).

I'm considering buying bp for deathmatch, but I'm on the fence about that weapon because if I get PJWS from the standard banner is a better weapon for him right? I'm thinking skyward at least gives some crit rate. Is it a bad option?