For City of Heroes Scrappers, the primary powerset is the offensive set that provides attack powers.
Broad Sword - A heaviest hitting of the scrapper sets. It is primarily single target damage.
Claws - Mainly single target but with a few AoEs, the claws set hits fast and has a lot of knockback attacks. It is not terribly group friendly as a result of the knockback.
Dark Melee - Mostly single target, dark melee has fast hitting, fast recharging punch type attacks.
Dual Blades - This set relies on combos to deal much of its damage. The set is poorly designed and ends up being weak.
Fiery Melee - A weak, badly flawed set at its core. The secondary effect (DoT) is unreliable and random. The attacks are slow animating and do poor damage.
Katana - Not as heavy hitting as broad sword, but the attacks animate and recharge faster.
Martial Arts - Mainly kick based attacks, martial arts does mediocre damage and adds some knockdown and stun effects.
Spines - Spines is primarily an area of effect set, with moderate single target damage. It adds bone-like spines to your character model, so make sure you like the looks of that before picking this set. It can be a lot of fun and is a very solid set.