How do you compare audio files?

I usually get the wav files in sync in an audio editor, without inverting them, and then listen for differences. I often have to keep moving one over slightly as the song progresses, if they're at slightly different speeds.

I agree with Aaron and Brian 100%.

Get them both in Cool Edit Pro (or whatever you use), line them up as best you can, and switch back and forth at various points in the song.

You'll develop an intuition pretty quickly when the samples when/won't line up. In general, if the waveforms don't look anything like each other, they won't stay aligned. If they do kinda look like each other, they're most likely from the same analog transfer, and they'll stay "mostly" aligned with only a little difference in pitch/speed between the two. And sometimes you luck out, and they stay aligned completely.

When they're aligned as best you can, you can easily tell if one if faded early from the fade on the screen. If one fades early, it's much easier to see than to hear.

I agree with A, B & C (that's, Aaron Brian & Crap) 100%. The only other thing I do besides this method, is to start the 2 different sources on my stereo system at the same time (one source playing on CD player #1, and the other playing on CD player #2 but going through my cassette deck where I can adjust the volume of that CD with the cassettes faders); I match up the volume so they're both at the same volume and both are playing simultaneously, I then use my receiver to switch back and forth between the 2 sources, and this makes it easier to hear slight panning differences and subtle mix differences, than if you do the other method above - because you essentially have one stream you're listening to, and when you go back and forth, it's real easy to notice that suddenly an instrument moved slighty to the left or is slightly lower in the mix (or not there).