Boxing will most likely always be bigger worldwide. A good boxing match where the fighters go back and forth and show crazy heart and determination is better than the best ufc match 100% of the time. There are not many sporting events as epic as a quality boxing match. UFC is cool and all, but it is too complicated and will never ever be "pretty." Mixed martial arts is too focused on the knockout while the best boxing is all about the battle.
The most beautiful things are clear and simple, why do you think soccer is the most popular sport in the world? It's a simple and beautiful game when played at the top levels. Two guys standing toe to toe firing rights and lefts will always be better than whatever the best UFC match will be. Boxing is fuked up in many many ways, but the beauty of a classic fight will always be there.