I prefer round but if you love a princess cut you could have them mounted in a drop wire setting. Not exactlty a "stud look" but the stones wouldn't twist and a lot of light would come through the back for more sparkle. I've seen princess drop earrings, 3 TCW, and they were gorgeous!
I prefer prong, more versatile for formal or semi-formal/cocktail events, or even a casual jeans and diamonds day. Bezel doesn't work as well in a formal setting.
I depends on the size of the diamond. If it is a smaller stone, I prefer bezel (gives a bigger earring appearance). If it is a larger stone, I prefer the prong set.
prongs allow for the most diamond exposure. a bezel encloses the diamond but makes a smaller diamond appear larger. both are beautiful in their own way.