https://english.stackexchange.com/questions/181745/which-do-you-like-best-or-which-do-you-like-mostI would use the above to ask for someone's advice on which they preferred of three or more choices, where the 'ranking' might go from least preferred to best. (this one, not at all, these two are ok, this one is very nice, but this one I like best.) In other words, good < better < best.
Most seems to me to connote a larger sample from which to choose. It is also asking more (to my way of thinking) for shades of interpretations instead of an authoritative opinion. Best limits the choices and the answer seems final.
- What kind of books do you like most?
I can see an answer like, I like sci-fi and mysteries.
However, I think that they are used fairly interchangeably.