I started with the standard overhead cast, but after a couple of seminars with Lefty, I gradually changed to a style more like his (although I don’t think he would agree that it is a style, but a technique for certain situations). I also have a little Chico Fernandez thrown in.
I agree with Zach, you should think of them more as techniques than styles. When I’m out on the flats I use a side arm “Lefty/Chico” technique, but its not appropriate for fishing small waters. Then I usually revert back to the standard overhead.
At some point you have to start thinking about developing techniques appropriate to the situation. When I’m in the kayak I cast with one technique, wading another. I even have a backhand cast that Lefty taught me for situations in which you have to hit holes in the flora behind you on your backcast to get a decent cast off. Now I even use the backhand cast for situations when I have a strong quartering wind from my casting side.