Your audio interface's A/D converter will almost certainly be better. Most USB turntables are built like junk and will have other issues such as wow and flutter. I had an Audio Technica and tossed it for a few reasons, including what appeared to be a lack of EQ.
A vinyl record needs to be played through equipment having the proper
RIAA equalization curve or it will sound tinny. Old stereo receivers had this built-in. I once tried recording direct from turntable-to-tape using a $20 Phono preamp from Radio Shack (supposedly with equalization) but the preamp itself sounded like crap. That's when I realized the importance of a true RIAA curve.
If I were to do this, I'd plug my standard turntable into a stereo receiver with phono inputs, then connect record-out/line-out from the receiver to a good audio interface (your Fast-Track?). Others have said this is the best way.