Yes, though the second way sounds more elegant. This is assuming you're meaning to say/write that the second person IS the best person to do the thing. If, however, you were asking a genuine question, then "who can do this better than you?" might be clearer.
The first is a most likely to be a direct question only asked of a person who has voiced an opinion that they are unsuitable for a given task, while the second comment could be a question or a form of flattery or question....Clearer versions would be geofbob's version for the question and "You are the best person for the job" for the flattery.
I've been looking at this again, keitra, and I think a slight alteration to the order of the words would also improve your examples -"who is better than you to do that?" & "who better than you to do that"?. (But I also agree with sft - if flattery is intended, then a straightforward statement might be clearer and easier.)