I know the differences in the structure of these 2 time signatures, but what are the differences about the auditory perception, aside from the fact that 3/8 may seem faster?
Both 3/4 and 3/8 can be Simple Triple (three beats in the bar) or Compound Single (one beat to the bar). Textbooks don't mention Compound Single much, but it happens all the time in real music - a fast 'one in the bar' waltz. A close relation of Compound Duple, a 6/8 (or 6/4) two-in-a-bar.
Historically, using 3/8 rather than 3/4 didn't necessarily imply a faster tempo. In modern writing, it probably does. Waltzes are usually in 3/4, an Irish jig is conventionally in 3/8. But it will be easy for those inclined to do so to find plenty of exceptions!
If you're transcribing a piece, there may be historical clues as to whether to choose 3/4 or 3/8. But there's not going to be a clear-cut 'right' answer.