I think both are grammatically correct, but I hear "more than" much more often. "Better than" sounds weird with "like".

I think - more than-

The word "better" is the comparative form of the word "good". The word "more" is the comparative form of the word "most". You could say that chocolate is good. I like it better than vanilla. Hope this helps

Both are fine.

Thank you. I need to use the phrase "by far" as well. Could you give me an example sentence with "by far"?