Beginner boards range in length from 6' to 6'4" max, with a wide template through the waist to the nose to make them stable, easy and forgiving. However, unlike the ocean, anything over about 6'4" is simply too long and cumbersome, and this inhibits learning, not encourages it.
For intermediates and experts, super short boards, low tail rocker and wide tails with tri fin, quad fin or V6 fin systems are perfect for really opening doors. Having a board that is fast on the realitively flat and slow riverwave means you can push yourself harder, get closer to the lip, snap turn faster and higher on the wave and remake the wave afterwards, do tail slides on non vertical sections, and 360's etc. Of course, a good rider can do this with any board, but even the best riders agree that boards made for the wave make everything smoother and more dynamic. In a word: Exciting.
As a general rule, you'd ride a board on the river wave that is 6" to 8" shorter than what you'd ride in the ocean.