I think it depends on a few things, like those you've listed, and also your ears and source as well. If you are playing not so great music files from your computer, then the Asgard might not make a big difference at all. But if you are playing high quality music files, then maybe you will see some improvement. That's where your ears come in. With me, I play 320kbps music files through the system, and with any of my headphones, the Asgard doesn't make a 'big' difference. There are times when I think I might be able to hear a difference, but that could just be placebo at work.
What I'm saying is, it sort of depends on the rest of your audio chain too as to whether a different amp will sound different. Just my thoughts, anyway.