I've spent some time with the battery pack attached, using regular C cells, not rechargeables. I don't hear any difference, comparing the same track heard with the battery pack and the OEM transformer. Granted, this is me making the change between tracks. I really should have my son or someone else change the tracks, and then switch places, so we at least have single blind trials, since I'm not sure double blind would be possible. But I don't hear a difference after about a half dozen comparisons.
I didn't hear a significant difference with the battery pack, others have reported better sound. I still believe I hear much better sound with my 3a supply. Could some one with the proper test gear measure the current draw of the E90 playing music hooked up to a 3-5a supply? This might shed some light on this situation.