Questions like these are best answered using double blind testing or direct measurement methods. I have read many double blind test results testing the difference between DACs and Amps. Almost all of these tests conclude that there is no audible difference between their low end option and their high end option.
Personally the DAC is importable because it processes the noise. As long as the amp is not introducing any more noise, if the DAC is noisy, then the amplified signal is noisy. When I had my Bithead, Ultra Desktop Amp, TEAC, and m903 all in one place I did some extensive DAC testing and really heard little to no difference. It was a 15 minute listing test per DAC and I used one DAC to feed the signal into the same Amp each time. I did hear some subtle differences doing direct A/B testing with amps using the same DAC for each amp. Some amps sounded a little more boomy, some sounded noisy at low volume levels, while others really lacked soundstage. This is especially true if you listen to a Bithead via USB and then run the same track into an m903. The Bithead was bright, did not reproduce bass well, and lacked the vast soundstage that the m903 was able to represent. This was most likely because the Bithead lacked the oommph needed to drive the DT990 headphones. In each of these tests I used a pair of DT990 ( 250 Ohm ) headphones and a pair of Polk Audio M5 monitor speakers.
In the end it is all about signal processing and opinion is rarely going to get you anywhere. All of our ears are difference, our perceived sound is different, and our listening expertise is limited. This creates a wide range of responses, but for me I had to do the tests myself to decide. I highly recommend you do the same or you are going to be left with opinions by other people who do not have your exact biology or experience.
When I look at gear especially for upgrading purposes I first look at the device that is producing the sound wave itself. In most cases this is a pair of headphones or speakers. The biggest difference will be heard here because these devices take an otherwise unperturbed signal and generate a varied wave form. This is due to materials, speed, size, and a whole slew of other variables. There was a test done a while ago with an iPod playing uncompressed audio through a low end amp into high end speakers and the audience was convinced they were listening to a $20000 system when it was actually a much less expensive system.
When I first look at purchasing an amp/DAC or even speaker/headphone I first look at the measurements because they tell me what I should hear. The harmonic distortion curves tell me how well the diagraph and resonator are constructed. The 300Hz and 30Hz square wave responses tell me how the headphone / speaker can handle multiple frequencies. The impedance curve is important because impedance affects current draw and voltage. This determines how much power is being drawn from an amp / source. I look at the Signal to Noise Ratio for DACs because this tells me how much noise the DAC can suppress.
Without going into too much detail each component does matter and some components can alter the sound in a big way, but none more than the speakers / headphones. If the DAC and amp are doing what they need to then the signal should be relatively unchanged up until it reaches the speaker. Assuming the signal does not change along the path is huge and without direct measurement leads to false conclusions.
Using a better DAC on a PC will drastically improve the sound quality because PCs are horribly noisy. When I first used my Bithead on my PC via USB I was amazed at how noisy my PC is without the DAC. Improving your DAC will generally lower the noise of the system allowing the amp to generate less amplified noise.
If you are in the market for some new audio gear perhaps tell us what you currently have and if you hear anything you do not like or if you have heard something better. We can easily make suggestions from there on gear that can give you a better listening experience, make the audio more neutral if desired, or even boost the volume if that is your problem. For me it comes down to noise, build quality, audible improvements which I test, and of course enjoyment.
Your owe it to yourself to make your own conclusions be it via measurement or audibly.
Edited by NA Blur - 10/24/11 at 3:10pm