Melting point is usually more accurate because it isn't so dependent on pressure. Also, compounds tend to have a sharper melting point range than boiling point range. You don't get problems with azeotropes either, although you will observe melting point depression if the sample is impure.
To measure a MP, you usually use a special aparatus that is made for checking MPs, but you can get away with a regular oil bath which you heat slowly until you sample, usually placed in a capillary tube, melts.