$100 is rough, $250 is fairly rough. $500 is probably a bit much, but easy. 

$200-$300 is probably fair, assuming you have to buy everything. A good soundcard (with a headamp) is probably around $100-$150, depending on what you get, and that leaves you another $100-$200 for cans; you can get something like the Ultrasone HFI-2400; the Zalman clip mic or something else you can fish out of a parts bin is probably sufficient for voice. The Audio-Technica ATH-AD700 get suggested like candy; I've never heard them, but I hear good things about them (and have for a long time). Note that I'm not in love with the Ultrasone, but anything that I'd prefer to suggest will run you $300-$400 just for the cans. I don't think any of them are "leaps and bounds" better than the HFIs for gaming, but for music and other tasks they are (and yes that's a qualified opinion).

As you seem to be more gaming oriented than "audiophile quality"-seeking, I'd suggest keeping your current headset and investing in the best sound card you can afford. For me, best sound card for $0-500 is easily the Asus Xonar Essence ST/STX; however, if you're a true gamer, you'll probably enjoy Creative's flagship models of the same price range more (due to their higher support of game-enhanced audio FX).

http://www.newegg.com/Product/Product.aspx?Item=N82E16829132010 Asus Xonar Essence STX (PCI-e with no ability to expand to 7.1 analog) currently $172 at Newegg

http://www.newegg.com/Product/Product.aspx?Item=N82E16829132014 Asus Xonar Essence ST (PCI with expansion to 7.1 with Xonar H6 expander card) currently $209 at Newegg

Both cards offer VIRTUAL 7.1 without expansion card, for headphones or non-analog surround setups.

Seriously though, 99% of people will not be able to discern a difference between your Turtle Beach headset and a more expensive Razer equivalent. The point of diminishing returns is reached for in-game microphone input MUCH faster than you'll see for audio output quality. Besides, in upgrading your sound card, you allow yourself to take that higher audio quality to everything you do on your PC that involves audio. All you get with expensive headsets is bragging rights at LAN parties and an ePeen raise, nothing more. I've been playing FPS games competitively for the last 10 years and currently use a wired XBox controller hooked up to a $2 first party 360 microphone. No one has ever complained about hearing me clearly during matches (whether I'm yelling at my team to do something or whatever), and I spent the $100+ I saved on better speakers. I also have a wired controller to play emulated games with now. To put it another way, "gaming" headsets are to competitive gamers what Beats are to true audiophiles.

Sennheiser HD-558 (50-Ohm) $150, like the ATH-AD700, but with more bass.

Asus Xonar DG, $30, PCI, comes with a half-way decent headphone amplifier and has Dolby Digital (Dolby Virtual Headphone).

Separate Mic, $20 or less.

I would disagree with your summary of Asus and Creative parts. Regarding the price difference; it's also a difference in features. Read the product pages, get an idea of what the extra money buys you. You should put more of the money into the headphones; they make a bigger difference. That said, you probably have to spend most of your $100-$200 budget on a soundcard to get something high-end that will also drive hi-fi headphones by itself. 
 

Quote:

Originally Posted by wuschelbeutel 

I've asked this question on a different board and everybody seems to have a different answer. Some say to spend the budget all on the soundcard, others say all on the headphones. It's pretty clear that either my current soundchip or my current headset represents the quality bottleneck and so far I have not found a consensus. I forgot to state: I play first person shooters 20% of my PC time, 30% of the time I'm either listening to my mp3's or, rarely, my CD's/FLAC's. I'll order a PCI-Express 3.0 mobo with my audio purchase. There seem to be both 15-30 dollar and 100-150 dollar Asus Xonar's out there - is the difference big enough to justify the premium price? Also, are the Xonar's better in overall sound and have higher compatibility, while the Creative soundcards have more problems, are generally more expensive, and have high end gaming sound?

The reason you're getting so many different responses is because there are an infinite number of answers to your original question.

Thank you for specifying what your habits are in your second post! It really helps to know what you have in mind, otherwise we're all just throwing out equally great suggestions that may or may not be right for you.

You mention a quality bottleneck in your current setup, but "quality" is very subjective. What do you want from an upgrade? More bass? Higher volume? More comfort? The list goes on and on, dude, and you'll help us help you if you explain what it is you want.

I agree on putting more money into your output device (in this case, headphones) if you're looking for audio quality. Since you specified a headset in your OP, though, I assumed you were just going to use what you buy for gaming. If you're indeed wanting an improvement in your audio quality, then of course you'll want to upgrade your headphones first, your sound card second, and your mic third (if at all). Coming from this gamer, though, you really have no reason to upgrade the mic you already have unless you are having problems with your Turtle Beach headset. 

Also, you don't need PCIe 3.0 for any sound card that I've seen. Your system will support pretty much anything out there as long as you leave a PCIe or PCI slot open for whichever card you buy.

Quote:

Originally Posted by wuschelbeutel 
I've asked this question on a different board and everybody seems to have a different answer. Some say to spend the budget all on the soundcard, others say all on the headphones. It's pretty clear that either my current soundchip or my current headset represents the quality bottleneck and so far I have not found a consensus. I forgot to state: I play first person shooters 20% of my PC time, 30% of the time I'm either listening to my mp3's or, rarely, my CD's/FLAC's. I'll order a PCI-Express 3.0 mobo with my audio purchase. There seem to be both 15-30 dollar and 100-150 dollar Asus Xonar's out there - is the difference big enough to justify the premium price? Also, are the Xonar's better in overall sound and have higher compatibility, while the Creative soundcards have more problems, are generally more expensive, and have high end gaming sound?

Usually better headphones make more of a difference then the sound card.

Higher priced Asus sound cards support headphones up to 600-Ohms, have a better DAC and have swappable op-amps (operational amplifiers).

The Asus Xonar Essence ST (with the H6 add-on) can provide the ultimate in analog 7.1 speaker sound.

Asus sound cards are more geared for great multi-media support.

Creative cards in general offer more support for gaming (one example is older games from the pre-windows Vista era work better with Creative cards).

The Creative Labs Titanium HD and Xonar Essence STX & ST (without the H6) are about equal in over all sound quality.

I prefer the Asus Xonars because the software is simpler, but still does the job I need and is easy to fix software problems (reinstallation).
 

Quote:

Originally Posted by wuschelbeutel 
If I get Audio-Technica ATH-AD700, is it worth moving from a Gigabyte Panther Point soundchip to a

ASUS Xonar DX 7.1 Channels PCI Express x1 Interface Sound Card

actually the better question is: buy a $200 headset (or headphones) and keep my soundchip (i dont know whether the gigabyte panther point im going to get will have a better soundchip than the one i mentioned above)
OR get a ATH-AD700 and a ASUS Xonar DX?

Save a few dollars, get the Xonar DG, the DG will power headphones just as well as the DX.