I've seen both several times. I actually liked Costner's Earp better than Russell's -- much better acted in my opinion. Quaid was remarkably good as Holliday, though not quite up to Kilmer. If it weren't for Kilmer, Quaid would've gotten a lot of recognition for his performance.
Sam Elliott was a way better Virgil Earp than Michael Madsen. I liked Morgan better from 'Wyatt Earp' (not sure who the actor was ... but I didn't care for Paxson). And, the love interest was WAY better in 'Wyatt Earp' -- the woman in Tombstone was an irritating party-girl and the love story entirely unnecessary. The woman in Wyatt Earp was far more charming and easier to see why Wyatt was taken with her.
The villains were much more memorable in Tombstone, though.
Overall, Tombstone is probably a better action move and pulp-ish western. But, Wyatt Earp is a better pure western. More of a western epic than the brief-in-time snapshot that Tombstone was. And, 'Wyatt' was a bit less cartoonish.
SnakeDoc