If you do someone a favour, you do something for them even though you do not have to.
恩惠 • I've come to ask you to do me a favour. 我是来请你帮我一个忙的。
If you favour something, you prefer it to the other choices available.
更喜欢 • The French say they favour a transition to democracy. 法国人说他们更喜欢向民主的过渡。