used to say that it does not matter which thing or person is chosen because the result will be the same:
It will be a difficult operation, whichever method you choose.
Whichever way you look at it, things are pretty bad.
used to refer to the member of a group of people or things that does something, is wanted, is possible etc:
Whichever player scores the highest number of points will be the winner.
You can either have the double room or the family room, whichever you want.
'Do you want tea or coffee?' 'I don't mind - whichever one you're making.'