When HDTracks sells a 16bit/44.1Khz vs a 24bit/44.1Khz, yes I can hear the difference, the 24bit being the better.
AFAIK, the difference between 16 and 24 Bit happens below -96dB, so for once you would have to listen at really loud volumes, and as many mics and preamps produce noise above -96dB, you can most likely only hear noise at a better resolution.
Regarding the original question, I wanted to "hear" high res (which I cannot, because my listening threshold lies somewhere shortly above 16 kHz). So I produced a differential track from the 48 kHz and 192 kHz versions of Paul Young's "Come Back and Stay". Which, if we can believe the advertising, was sourced from the original 2-inch master tapes, so we could expect the full range of analog recordings.
The result is a signal with significant information between 22 and 30 kHz, the peak volume being around -82.5 dB (at 22 kHz, way lower beyond). I normalized the signal and then transposed it so that 20 kHz are 1 kHz in the transposed track.
The transposition creates a lot of artifacts, so this is nothing more than an approximation, but I was just curious what I am missing. What was left was peak signals from snare hits and noise in a repeating pattern which I assume is tape hiss.
So that is the difference hi res makes in this specific example: ultrasonic snare peaks at 22 kHz at -82 dB volume, and even lower volume tape hiss between 22 and 30 kHz.
I can only urge everyone to make such experiments yourself. It is not so hard if you already are able to rip audio to WAV and use Audacity for the audio transformations.