For looting imperials: It's imperial property, its tagged with serial numbers, some even logs fires shot and communicate if they can to the holonet; this goes for some blaster pistols, imagine the information overload if this was done with stormtrooper rifles? Still, the imperial stormtrooper rifles is not something you'd want anyone see you with, carrying it casually... bad idea.
Looting armour? well, if you blasted the poor trooper with one shot, I'd maybe let you use it, but I would considered it Sundered at least once, if not twice. If many shots were fired, it'd be more or less useless as protection. Of course different with brawl attacks.
Also remember Encumbrance, they'll start dropping stuff quickly once they get lots of setback dice to agility and brawn related checks, and when they lose their free manoeuvre each round. Oh yes.
+1.