If we're talking about *just* the DtoA stage there will be hardly any difference that you can pick apart with your ears (this is not mysticism, it's science) - they're all going to be transparent unless one of them is damaged or not performing to spec. If we're talking about the line-driver that you hook your headphones into, that can get a bit harrier; it depends on the load and what it demands. Any two amplifiers that can meet those demands (doesn't matter how much they exceed them) will be transparent with respect to one another. The integrated solutions for many computers and the line-stages for many DtoA devices (or source components, like CD players) are usually not very good at driving more complex loads (this is where the mantra of "hard to drive" comes from) - you'll usually hear FR abnormalities or (if the thing has no power behind it) clipping distortion.
In terms of "how much do I have to spend to get it external" - probably hundreds, if not thousands, of dollars. This is because boutique products have ridiculous mark-ups despite using more or less the same parts (in other words, the best DtoA converters in the world from Cirrus, TI/BB, AKM, etc are only a few dollars a piece; when they're found in computers, AV receivers, Blu-ray players, or mobile devices they usually don't command a huge-markup, but when they're found in standalone DtoA boxes or hoity toity CD players they suddenly become multi-thousand dollar "premium and rare" parts).
Most of the external devices ("USB DACs") being mentioned will "beat" the integrated audio solutions and soundcards not because they're somehow more "audiophile" (most of them are actually outclassed in this regard; not that it matters), but because they usually have output stages that can deal with more complex loads; they're designed to be amplifiers. That makes a lot of difference. It doesn't really matter what DtoA you use (or what cables you use, or how it gets power, or any of that) when it comes to what your final component is (speakers, headphones, whatever) - that's a line-stage device, and whatever sits before the final load is ideally going to be designed to take a line-level signal and produce an amplified output (in other words, an amplifier). This can be anything from a little headphone amp (which I like because it means less wasted power) to a huge power amp with a headphone jack (which will probably use more power (by a factor of hundreds or even thousands - perhaps even ten thousands if you're using a modern AV receiver)) than it really "needs" to use for what you're driving and the output power you're demanding, because most of those big amps will drive the headphones with their primary amp stages run through a resistive network (to protect the headphones, your ears, and potentially the amplifier) which will sink a lot of voltage and waste a ton of power - for example if you have a 200W/ch amplifier driving your headphones (which probably need 0.02 mW/ch (1000mW = 1W)), the amplifier itself is probably going to be seeing a few wpc of load, as if it were driving speakers - that wastes A TON of power).
So having said all of that - a headphone amplifier can make a whole lot of sense when hooking up headphones to your computer (or whatever), but it doesn't have to be incredibly expensive or incredibly complicated.
For some graphs and magic:
http://www.afrotechmods.com/reallycheap/soundcard/sennheiser.htm
http://www.meier-audio.homepage.t-online.de/tipstricks.htm
http://www.avsforum.com/avs-vb/showthread.php?t=1294455 (this deals with full-size amplifiers for full-size speakers; you can ignore everything about room acoustics, placement distance, and so on - I'd also suggest pulling sensitivity values from InnerFidelity when available, as many headphone manufacturers (like AKG) have this nasty habit of rating at 1V instead of 1 mW (it gives you higher numbers and can make moderately unsensitive headphones look very sensitive (like the K701, which is around 93 dB/mW, but the specsheet shows it at something like 100 dB (again, into 1V, but that part is a footnote); of course once you start looking at the output abilities of most headphone amplifiers relative to what most headphones need, you'll probably realize that things like clipping are probably never going to enter into the equation).
