geez, this thread has been all over the place................
quite entertaining really.
haha, anyway, Abe21599, in answer to your question: "is there gonna be a comparable difference with an amp if my source has variable quality music?"
With the HD650s the answer is a very resounding YES! those are high impedance headphones and demand power! sending them out of the mini jack on your computer will produce less than stellar performance especially in the bass simply because your computer doesn't have the power to drive those suckers. To give an over exaggerated but effective analogy: it's like trying to drive a massive MONSTER truck with gigantic tires with the engine of a Toyota Prius, what kind of gasoline (bitrate) you use at that point is kind of irrelevant because the engine wouldn't be able to move the monster truck anyway.
(^Amp^) (^HD-650^)
So, now that you have your new amp, you have just upgraded your engine significantly, and should see/hear a difference in SQ. Now you can focus on what kind of gasoline (bitrate) you're going to use for your new beast, of course higher quality gas will produce better results, how noticeable and if it is worth it is up to you.
you also asked: "what am I missing?" I would like to let you know that for the enthusiasts/audiophiles that own the HD-650s, many of them buy aftermarket cables to improve the sound quality even further. In the Monster Truck analogy above, this is like buying better tires (better is a subjective term, better tires for monster trucks could mean bigger, stronger, better traction). Cables usually improve fine detail and bass, with silver cables even more details can be heard and the treble and midrange usually change for the better.
here is a review of 3 different cables by moon audio tried on 3 different headphones by Sennheiser and I found it very interesting (the HD600s, HD650s, and HD800s):
http://6moons.com/audioreviews/moonaudio2/dragons.html
cables are optional and are only if you want to get the last 5-10% of SQ from your headphones. If the improvement is worth it for you then great, if you are happy with what you are getting from your setup right now without cables then I am envious of you. I bought cables for my AKG k702s because I have a problem, haha. (they do make a difference though.) Mine cost $275.
How are your HD-650s treating you? you must have had some listening time with them and the new amp right? we are curious about your impressions, I am at least.