My personal preference is Unarmed, because you typically don't need as high Strength. Each of the two has very effective weapons, Thermic Lance and Chainsaw are my favorites for Melee, while the Bear Trap Fist from Dead Money is my favorite for Unarmed (Why, I don't know. It's beaten statistically by quite a few other weapons. Still works great though.)
I really enjoy the cosmic knife clean from dead money. It has axtra critical and limb damage and has a decent attack when its fully repaired. The special move in VATS "Surgical Strike" is fun to use.