Ideal77, if you'd asked whether a particular recorder performs better at one sampling rate than another, you might have gotten a clearer answer. But since you asked about the difference in general, as you can see, the discussion tends to become quasi-theoretical. Since so many myths about digital audio are still in active circulation (several of which have already appeared in this thread), the answers that you get (a) won't usually agree and (b) even if they do agree, might be flat wrong, and (c) even if they agree and are scientifically accurate, still might not help you very much, if you're just trying to decide what sampling rate to use for your next recording, or which recorder to buy.
One thing I can simplify for you right away, though: You mentioned the number of bits per sample. That number, whether it's 16, 24 or 3.14159, has nothing to do with sampling rate. An oversupply of one can't help an undersupply of the other. The number of bits per sample, if it affects anything at all, affects ONLY the dynamic range--the maximum difference between the highest possible sound level and the noise floor of the recording. It can't affect anything else unless the design of a system is hopelessly broken in some way.
It's not like with MP3 files, where there's a single "bit rate" (such as 96 kbps) and the higher that bit rate, the better the sound quality is likely to be (up to a point, anyway). Instead, there are two separate specifications--sampling rate on the one hand, and "word length" or "bit depth" on the other--each of which influences a different, mutually exclusive, dimension of sound quality.
--best regards