Belay plates are flat pieces of metal with holes for one or two bights of rope. Usually the openings are two different sizes, so you can belay with a thick 11 mm rope, as well as a more streamlined 8 mm. However, if you are using double rope technique, two ropes of equal size won't run consistently through the different sized holes. Plates are extremely easy to use, but aren't known to be smooth rope handlers, since the rope is kinked at a severe angle to allow maximum friction in catching a fall. However, they are virtually indestructible and don't wear on your rope as much as other devices.
Tubes are a more modern, technical version of the belay plate.
They have two equal sized holes, so you can switch from single to double rope belays with ease. However, the rope-bearing surface is smaller and thinner than a plate, and is tougher on the rope's sheath. The tubes with an accordion pattern in the metal tend to disperse heat faster than flat sided tubes or plates, so they don't get as hot during long rappels. Since tubes are shaped like an truncated pyramid, they hold the rope away from carabiner better than their plate cousins, allowing for greater lock off friction. Tubes are adequate for rappelling, but they tend to lock up, providing a jerky descent.