Are USB headphones/headsets inferior to regular ones?
The interesting part of a USB headset is the fact that you're going to have to go from digital to analog audio at some point during the transition. The problem is, good D/A converters are not cheap - last I checked, the majority of USB headsets were made of very cheap components that do not account for high fidelity listening. This can create sound coloring that is satisfactory to 95% of all listeners, but a discerning ear will be able to tell. So to answer your question, unless there's a niche headset out there with excellent converters, it isn't going to sound as clear/transparent as an audio interface with dedicated/premium converters like the Apogee Duet (when using a normal audio headset).
Just for some more background, I produce music and have been doing so for quite some time. I've run the gauntlet on different audio interfaces, ranging from consumer to full professional gear. Currently, I use the Apogee Duet as my audio interface for recording and playback. When I don't have the Duet with me and am running off of my laptop sound (which is a RealTek chipset), there is an immediate difference in response to my earphones. The difference between the Duet and the RealTek is that the Duet is much more transparent in that it is playing back the audio with as little effect on the signal as possible. The majority of that happens in the D/A converters. The Duet carries a hefty pricetag for this ability - I just can't see a $30-90 solution that includes headphones, microphone, and A/D - D/A as having the type of quality as a prosumer device. Probably because Joe Consumer doesn't really care, as long as it sounds good.
Edit 3: More information = better answer
By reading your responses to comments and what we have discussed, the short answer is No, there are not limitations of USB that jeopardize quality of sound versus onboard or internal soundcards.
I've just found this post on Ethiopian Review which lists the pros and cons of both. It lists these as the negatives for USB:
The main negative of USB headphones is that they can be finicky in regards to being bumped or unplugged. If you unplug a standard audio jack headset, it can be plugged back in and immediately be receiving sound. However, due to the USB headset being an actual device that is technically installed, it is not so immediate. The second part of this problem is that sometimes it can be difficult to get sound back in a program that is already operating, forcing a restart.
The second negative of USB headphones is that they take up a USB slot. This problem is generally easily solved, but for those with a large amount of USB related equipment it may become an issue.
But doesn't really mention the sound quality.
I own a couple of headsets, USB and non-usb. The USB one I have is the Creative Fatlity ($40). As for regular ones I have Bose Quiet Comfort (i know a stupid impulse buy) and a cheapo $20 altec lansing.
To answer your question first, no there's not much difference that I can tell (I am not a sound aficionado by any stretch). Though I feel that the USB sounds better cause the one I have stops outside noise better :). Though the Bose feel/sound even superior due to even lesser interference from outside :).
Here's my take, when you need multiple audio streams to different devices or quickly need to switch from speaker to headphones, then usb is great. However it also becomes single use, i.e. only with a PC/laptop. This is a big limitation, if you get a nice headset and want to use it with an mp3 player or stereo or share two headsets on a laptop while watching a movie, it can get difficult. AFAIK there are no USB to standard headphone jack converters.
But if you get a decent pair of analog (i.e. regular) headsets you can use them with majority of the devices in the world and no problemo! So my recommendation is still get the regular pair unless you have a specialized role that can be filled with a usb pair.