It's not the interface, but that more USB headsets have built-in DSPs that filter out noise.
Most standard headsets (mini-DIN connectors) do not, and are geared mostly for voice comm. and basic speech recognition.
However, as general purpose CPUs get more powerful, you'll get better recognition from the software engine itself and the fancy headset DSP becomes less relevant. I think people (with disabilities, for example) who purchased dedicated speech recognition hardware a decade ago had to pay into the 5 figures for what is commoditized today and available for any PC (Pentium3 or later, realistically).