Actually, given my choice of armament, I would use both a rapier as well as a 10 to 14 inch dagger in the classic European style. You would be cinnamon toast on a stick.
I've been on both sides of that equation, and had victories and losses with either weapon choice. Prefer the rapier and buckler, myself.
I still contend it is not the weapon, but the weilder which determines victory.