I would say that they basically have the same meaning but that "fair" is a little more neutral and common and "impartial" is more specifically stating that it is without bias. Fair can mean acceptable, okay, reasonable etc. So really... only subtle differences in tone and sometimes some variety in terms of which contexts they might be used in. One is not necessarily better than the other. It depends on context. "fair" is the more commonly used word, but it also has a wider range of uses.

fair= just and impartial= unbiased. (Usually referring to some aspect of the legal system, such as a jury, a hearing, or a judge.) Example: The man felt that he had not received a fair and impartial hearing. His lawyer demanded that all judges should be fair and impartial in every instance.