I use it in every game. I like the variety. You have to pay attention to learn the behaviors/personalities of your neighbors over the course of the game, which I think can actually be more difficult, at times. It makes me much more reluctant to ally early, for fear of hitching my wagon to a surprise warmonger. You also experience some unusual, but difficult, combinations -- like in my current game I'm facing a war-mongering Gandhi with super-fortified cities, and he is a very tough nut to crack. I fear that his war with me, if it drags on much longer, is going to cost me the game. But somebody has to stop him.
I get the impression, purely anecdotally, that random personalities overall are more "moderate" than the default personalities. Only about two or three civs per game really stand out as having unique personalities. There's usually one clear warmonger, one clear CS-monger, and maybe one science-pusher, but most of the civs seem to blend together into an unremarkable, moderate style.