Do what you like is most likely to be used with a tone of annoyance, indicating that someone isn't listening to your advice and intends to go their own way, so you get annoyed and say 'do what you like'. However, if you are encouraging a friend to do what they think is right, perhaps to resist advice or pressure from someone else, then you would say, 'do what you think is right'. The two phrases on the surface, appear very similar, but convey two very different tones.

if said in a negative tone it can come across as rude. It shows that you have no interest in what the person whats to do, which can be taken in a negative way. Although if said in an indifferent tone, in a friendly way it is not very rude. Your better off to say "If you would like to" or "Do what you feel is best" or something along those lines