-moz is the proprietary css for all Mozilla-based browsers (such as Firefox, Camino, Flock etc.)
-webkit is the proprietary css for all Webkit-based browsers (such as Chrome, Safari, Mobile Safari (iPhone/iPod touch), Shiira etc.)
Internet Explorer is kinda the annoying kid in the branch, and used neither Mozilla or Webkit. Instead Microsoft built their own thing that sucks badly, and sadly costs us developers the most time.
Regarding the rounded corners though, I’d say, unless they are part of your brand of corporate identity, I recommend using the -moz and -webkit commands. The only thing that will happen in Internet Explorer is that those corners will be square. Yeah, big deal, nobody cares about that.
That saves you from loading any unnecessary images or code.