What exactly is looking poor on your current skydome ? Does it look blocky, distorted, or are the colours off ? Chances are, that the textures you're using are just not appropriate for a (rather large) sky, or that the projection is wrong. Can you post a screenshot ?

A skybox is a very popular and easy to implement technique. And it can look really good, usually much better than a dome. In the end, it all depends on the textures you have. Although they're not always easy to find, make sure you're using the highest resolution ones you can get.

And if you can't find some good skybox textures, you can get great results quite easily by using Terragen to create them.