Actually it depends on the context. If we know the choices, "which one do you choose ?" is the best answer; if we have no element about the choice, or if there could be several choices and we absolutely don't know if the subject will choose one or several things, we'll say "what do you choose ?"
The grammar structure of "what's your choice" is different from "What/which do you choose?" "Choice" is a noun and emphasizes the item being chosen. "Choose" is a verb and emphasizes the act of deciding/choosing. The better translation for "Qual você escolhe?" is "What/which do you choose?" since it follows the same sentence pattern/grammar.