to me it mainly depends on whether it's tube or solid-state. Both versions saturate the guitar tone in their own way. It's pretty safe to assume that you're talking about a tube poweramp though, so what I hear from poweramp saturation is a general thickening of the tone, a slight rounding-off of the pick articulations, and a little bit of added distortion/overdrive that sounds different from the amp distortion.
In general, I love poweramp saturation!