I don't mean any offense at all, but right now I seriously can't figure out whether to blame myself or you for wasting both of our times, even if it's just a couple minutes.
Without the amp, you would be plugging the headphones into what? An amp isn't like an effects processor, EQ, or something like that. To get sound out of headphones, you're running them out of some type of device. To gauge the performance of another amp (here, the O2) relative to that, you need to know the characteristics of the original device, how good or bad it is (and in what ways) it is for driving headphones like that.