Without rider intervention I reckon long and short boards would go the same speed if all other variables were equal. Short boards would accellerate faster but have less momentum and so slow down quicker than longboards due to differences in mass and drag/friction/resistance.
But the biggest defining factor involved is the rider.
Think of it as going on a normal swing.
Without moving whilst you swing you have no part in helping it move, other than your mass being affected by gravity - so the swing will stop moving quite soon.
But when on a surfboard on a wave, what the surfer does massively affect the movement of the board - like if you stand on the wooden swing and pump whilst moving you can get the swing to go forever or even get the thing to go right over the top if you want

.
This pumping action is the same as when a surfer pumps on a wave to go faster. It is quite simply using gravity to generate speed - you make yourself heavier on the bottom of the pump and lighter at the top. And it is this thing above all else such as size, weight of board, rail shape, rocker shape etc. that will affect the speed of a surfboard - unless we are talking about the rare situation of riding a 30ft big wave where you are just gunning it straight down the face, but even then you could gain an advantage by pumping when first taking off to accellerate faster.
So bassically I'm saying its the surfer that powers the board more than any other factor - long or shortboard. But gravity, wavepower, rail shape, rocker shape, tail shape, board mass etc. all have some affect but not as much as the rider.