I like the button because it's easier to click with something other than your thumb. I have to say, I like the crisp noise of the box a bit better, but not enough to go back. The thumb tabs can get icky (rusty) too.
I've got both, and it depends on what I'm doing. The box clickers are def cheaper, so I've got several of those, and got them stashed everywhere. The button ones are really convenient sometimes if you need to (for whatever reason) click with your foot - you sure can't do that with a box clicker. I went to a training seminar today, and with a room full of people working their dogs, a few with the quieter button clickers weren't getting very good results - so they ran and got them box clickers. The dogs just couldn't hear the 'click'. Presto, instant improvement. Times and places for everything.