Do you mean an amped RE262 vs an unamped A161p? I didn't hear a whole lot of improvement when amping the A161p (maybe a little more control through the bass frequencies, but it sounded pretty great straight from my iPhone).. let's assume a head-to-head with both being amped..
A161p is a hair faster and, obviously, more neutral.. but other than that, an amped RE262 is the better phone in every technical category. Soundstage is larger, better dynamic range, more natural timbre, better microdetailing and extension. The A161p's treble is a little crisper and airy (where the RE262 is smoother and a little laid back).
That being said, they're voiced quite differently. The A161p going for neutrality & balance while the unabashedly colored RE262 is all about a liquid, smooth, lush, airy, almost ortho-like midrange presentation. The A161p can dig surprisingly deep for a single BA phone.. it's smooth and natural sounding, but not to the extent the RE262 is. Both are very special and offer tremendous value at their price points, but I think the RE262 is truly one of a kind. I've heard nothing like it.
Edited by FlySweep - 6/7/12 at 10:31pm