http://pdf.crse.com/manuals/4253437131.pdf
This should get you the pdf for the Sony amp.
I found the pdf for your amp at manual shark.
This is a description of your card.
http://www.asus.com/Multimedia/Audio_Cards/Xonar_D
It turns out that your card is a multi-media card which will send a digital signal to a home cinema reciever. It may even put out more than one channel in an internal digital audio converter. I had a computer sound card an Audigy which did that. The problem here is the Sony amp does not have any type of digital input. You may want to find a D/A converter down the road and try using it with your computer sound card.
Some D/A converters now have headphone amps built inside. Also you could by pass your computer sound card and get a USB to D/A converter which has a headphone amp in it and just plug your headphones in it straight.
If you don't want to spend a lot of money your sound card will be able to also be plugged into other amps to try to see if you can get an improvement over the Sony amp. You really just have to try a bunch of combos and just listen to what it sounds like. If you can not tell the difference between the headphones being plugged directly into the sound card and the sound of the headphones into the Sony amp from the sound card then maybe there may be very little difference. That can happen at times.
Nowdays there are really more choices than ever and I have not tried many of the low cost or high cost D/A converters which allow you to get audio straight out of your computer. At one point I had an E-MU 0404 sound card for doing computer audio music recording. I would record music and monitor it with an old Pioneer amp and headphones kind of what you are doing now. I did some tests and felt the 0404 was just not getting me the sound I was looking for and left trying to get computer audio with an internal sound card. I like the sound of my Nuforce Icon now running it out of the computer USB and I plug the headphones right into it. It has the dramatic sound I was always looking for with the EMU 0404 but was somehow not able to get. So I would agree that a lot of different computer set ups can have a different sound and you can of have to try different things until you find YOUR sound in the end.
That talk of the month around here though is that your going to get maybe a better sound going optical out of your computer or even using the S/PDIF Digital Output :44.1K/48K/96KHZ @ 16bit/24bit you are getting out of your sound card.Maybe the best not usingUSB but putting it into a D/A.