The way I see it, Arbiter is a very legit weapon for a DMC game because it makes you think about how to use it instead of simply "go in, switch weapons, and hit buttons." The best way to use the axe seems to be as a poke in between combos or to end a combo with a heavy blow. It surprisingly chains really well with other weapons, so you can do something like two hits with one weapon, quickly change to Arbiter, get a hit in, and then switch back to another to keep the combo going. But the only way I would actually commit to do an entire one-two-three combo with just the Arbiter is when I only have like one enemy remaining and I'm not in danger of getting hit by another in the middle of it. And yes, Arbiter's blows give a crap ton of style meter.
But yeah, I'm with most people here when I say Osiris is the best. Reason? Crowd control and air combo galore. I mean, keeping three or four enemies at once in the air while spamming the crap out of it is so broken. You can literally kill an entire group of demons without touching the ground once just using Osiris, won't give you much style tough since you will be using the same moves over and over. Good thing they added things like enemies that can hit you in mid air, or those that can only be hit with demon weapons, to counter the scythe. If it wasn't for this I could have probably beaten DMD mode using nothing but that weapon XD