In the real world it doesn't make sense to present a list of choices when asking someone's favourite (colour, song, food, whatever). There are many possibilities, and people have varied tastes; unless your list was exceptionally long, the actual "favourite" probably wouldn't even be in it.
As this Google NGram shows, the standard form is "What is your favorite color?" (it's the same pattern with British spelling). The word "which" occurs too rarely to graph in this construction.
But when you ask someone's preference, this is often in the context of a limited number of options. As this NGram shows, which and what occur equally often before ...color do you prefer?.
In short, what is standard with "open-ended" choices, but which always implies specific options...
"What do you want?" (really does normally imply you can answer with whatever you want).
"Which do you want?" (always implies your possible responses are limited in some way).
In OP's context, only what is correct for text input boxes. Where "multiple choice" possibilities are displayed, both which and what are acceptable - it's just a matter of stylistic choice.