Rapier - a lot of things are weak to stab. It's faster than a CLS. Any DPS breakdowns will show that CR has much better DPS than CLS. For those who say it sucks at bossing.. I find myself doing better than people with CLS even at Bandos. I'm 99 att/str/turm/ovls, but still.
Rapier is best overall fighting weapon (i.e. for slaying, training ect.).
CLS I'd say is better for boss fighting.
Maul is debatably the best for PVP, but all the chaotics work well in PVP so it's close.
Rapier because fast as a whip and has a high stab bonus.
Comparing it to CLS, in PvP, if you;re using rapier, opponent has time to eat one food, CLS on the other hand, opponent can eat 2 pieces. Rapier > CLS