The biggest thing affecting just ski performance is: Bindings are made to keep your boot in one place on the ski. So, a shitty binding is one that doesn't do that (your boot moving in any direction with respect to the ski is bad).
Beyond that, there are some minor differences that come into play, but are preferences (they don't make a binding shitty or not).
1. How far the binding lifts you off the ski (farther = better carving, closer = more stable on landings)
2. How the binding tilts your boot. Some bindings have a higher rear plate to push you forward to help engaging the edge.
3. The area of the ski the binding attaches to. A shorter footprint (Look/Rossi) lets the ski flex a little more naturally.
There are other saftey issues when discussing how shitty a binding is, but they don't neccessarily affect your skiing.