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.