Clearly, the best action star is Bruce Willis. Why?
Much like Statham, he's cool and a badass. He's also a talented actor who is capable of more serious roles. However, like Arnold, I guess, he can have fun with the roles and play more out-there characters. Some of them are crazy, some of them are guys who don't take the situation seriously. But Willis provides a wide range of character he can play and play them all very well.
Alternates?
Will Smith is good and has a decent range, much like Bruce Willis. But I have yet to see him hit his defining action film. If anything, he's competent but hasn't hit the high point yet.
Jackie Chan is old, but every movie he is in is fun to watch (with the exception of a couple of the more recent films). A lot of his older stuff is comical not only because of poor dubbing, but also because of the slapstick humor incorporated into the fighting, which is pretty awesome. While not being as skillful as Bruce Lee or Jet Li, I've found him at least more entertaining on many different levels.
Nicholas Cage is... interesting. Not handled properly, you have a guy trying to play crazy when he likely shouldn't be. Handled properly, his crazy personality will shine just when you need it to and bring his characters to life. I think Kick-Ass best highlights just what kind of fucked up people Cage is capable of bringing to life on screen, and that's probably one of the tamer action-based character's he's played.
Lastly, Liam Neeson anyone? There are probably other names that deserve to by on my list, but I think I'll give it to Liam. This is a guy who was able to play Oscar Schindler. Since then we've pretty much been cool with letting him do whatever he wants and not judging him for the roles he takes. Some roles have landed him interesting action jobs. Taken was surprisingly good when it came out and he's had several others. While his action roles take a heavier acting tone than Chan, Willis, or Smith, Liam will always deliver a solid, kick ass performance. If none of the five names here are considered better than Schwarzenegger or Statham, then you must be crazy or just have terrible taste in film.