I've used both type boots but now currently have just the boot type. The stocking foot like RdFx stated are good if you do a lot of walking. They move around less on your feet and make moving around just easier. I used mine trapping creeks with sand bottoms walking accross pastures to get there. The ones I had didn't keep my feet as warm as my boot types but were ok because I was moving. The main reason that I've stayed with the boot type is dealing with the mud here. The boots I laced over my stocking foots picked up a lot of mud. Sometimes when I'd get back to the truck I'd be mud from the knees down. The laces on the boots I used would freeze and I'd have to waste coffee from my thermous to untie my boots, or just get in the truck and let the heater thaw them.
I deal with a lot more mud where I use my boots than sand or gravel.
Mac