In Tombstone, when Wyatt Earp joins his brothers Virgil and Morgan in the eponymous town in Arizona, he finds his reputation as a lawman has preceded him. He insists he's left all that behind him; all he wants now is to go into business, earn a comfortable living, and conduct a quiet, peaceful life. But the conspicuous lack of law and order in Tombstone prompts Virgil and Morgan to step up as U.S. Marshals, and their attempt to enforce an ordinance against carrying weapons in town turns into the infamous gunfight at the OK Corral. When Virgil is later crippled and Morgan killed, Wyatt embarks on a messy vendetta that bears very little resemblance to law and order.
Wyatt Earp covers a greater span of the man's life, from teenage longing to join his brothers at war to an old age still seeking new horizons in yet another gold rush. The Tombstone story is given a lot of time, but so is the leadup to it in Dodge City, which the earlier movie took as a given, assuming that everybody knew that legend including the viewer.
The films have invited comparisons to each other since they first came out, of course. Doc Holliday is probably the most compelling character in either one; Dennis Quaid is almost unrecognizable in the role, but Val Kilmer looks like he had more fun with it (point for Tombstone). It's hard to do better than Sam Elliott's "Best Mustache in a Supporting Role" as Virgil (point for Tombstone again).
I may as well stop counting points and just admit that I liked Tombstone better. It seemed more focused; Wyatt Earp didn't seem to be able to figure out what kind of movie it wanted to be, or what kind of character Wyatt was. The plot was clearer in Tombstone, and in spite of the massive number of speaking roles I didn't need a scorecard to tell the characters apart.