"Who are your favourite bands?"
"What are your favourite bands?"

Are both sentences correct? If not, which one is better? why?
Both are acceptable, although #2 seems a little more correct if you think about it for a while.

To some extent, I'd say it depends on the band name.
eg You can say 'Mick Jagger is a Rolling Stone' or 'Ringo Starr is a Beatle', but it doesn't sound quite so right to say 'Angus Young is an AC/DC'.

Best wishes, Clive
Thanks a lot, Clive