Booties for better grip and protection from rocks and sea urchins and stuff, and walking over hot sand on 40+ degree days.
I prefer a mid-height boot because you can seal it snug around your ankle. That stops sand getting in when you're walking into the water. In a shore break you need to lift your feet off the bottom to stop the sand getting blasted into the shoes.
Avoid a low cut ankle because there is nothing more painful then getting sand and broken shells between your toes inside a boot. Of course that doesn't apply if you don't walk over deep dry sand.