Crossfeed (not "crossfade" as you called it, which is an audio mixing term) and balanced amplification are completely unrelated, not sure how you arrived at your "both are methods of achieving the same end" conclusion.
Crossfeed is the adjustment of allowing a stereo signal to "bleed" into both channels to replicate speaker listening, because on headphones your left and right ears hear only the left and right channels respectively, while on speakers both ears hear both channels.
On a proper balanced amp (i.e., dual mono, not one with phase inverters), the amp internally replicates two amp circuits in each channel for true balanced amplification of L+, L-, R+, and R- signals.
http://en.wikipedia.org/wiki/Crossfeed
http://en.wikipedia.org/wiki/Balanced_audio
The typical sonic result of balanced audio is higher SNR / lower distortion, faster slew rate (translating to improved impulse response), and subjectively, usually more precise soundstaging and more clarity throughout the spectrum. You won't get any of those through a crossfeed adjustment, which will only bleed (or "blend") the channels to a degree.
Edited by Asr - 11/10/11 at 2:10pm
