Suede on shoe soles refers to the rough, unpolishable surface of a soft (chromium salts) tanned leather. It is either the inside surface of the skin, or more likely the leftover underlayer after the top layer is split off - so pieces are often called 'splits'. It should grip the floor a bit (when the nap is raised with a sharp brush) but still allow you to slide and spin when you want to.
Grain leather, as used on shoe uppers is the smooth polished stuff - the outer layer of the skin. It wouldn't make very good soles. (Patent leather is grain leather coated with a plastic-like substance to give it a permanent shine)
Vegetable tanned leather is very hard and slick - it's often used on street shoes but wouldn't provide enough traction for comfortable dancing on a wood floor. (Going outside and scuffing your feet back and forth on the sidewalk has been recommended as a means of getting a little extra traction for unexpected social dancing opportunities)
Rubber is usually too sticky for dancing, but some varieties may work in some cases. If a rubber sole sticks when you hadn't expected it to, there is the possibility of suffering at least a knee injury - hopefully only a temporary one.
The original poster seemed to be having slipping problems. One thing to do is to be really merciless with the shoe brush, and make sure it is a sharp one - some of the ones available are really made for cleaning the grit out of metal files, and so aren't sharp at all. Also the floor in question may simply have too much wax. In extreme cases, I've heard of people who had to do demonstrations on dangerously unsuitable floors resorting to using part of one of the anti-slip pads sold for street shoes on their dance shoes. There's one floor that used to be so waxy a roll of duct tape would be provided at classes - you could stick a piece to the sole of your dance shoe (shiny side on the floor) if you got really desperate, but it usually would fall off before the end of the hour.