That one is easy for me. If they get mutated from a science experiment I use science because all the data to replicate it is there. If they are born with it, and its not natural for their species, then its mutant as they wouldnt be able to replicate it under most circumstances.
Batman could go either way however he makes more sense as technology to me. Without the bat computer he would never find crime fast enough. When enemies are stronger then a normal human and he doesnt surprise them he always has to rely on something else or he loses, like when bane broke his back. I'm pretty sure non of his contingency plans say go punch the guy bare handed except for maybe green arrow. He relies on technology and is only able to fight normal people without it. Anyone super powered without tech hes either going to be useless or require another hero to follow his plan.