Highly dependent on conditions. You have to consider the force balance between friction derived from suction and friction derived from normal force, which is dependent on the weight distribution over the surface area of your skis/board.
When your skis (or board) slide over frozen snow it will melt a microscopically thin layer of snow based on the local heating derived from friction. Friction is dependent on the normal force at that location which ultimately depends on how much surface area you are sliding on for a given rider weight. For a constant weight, more surface are will reduce friction, thus faster (to simplify).
Skis/boards also experience suction based on the liquid layer of water between 2 solid bodies (snow and polymer). Suction, to put it as simply as possible, comes from the high surface tension of water.
Bottom line: if you want to determine if boards or skis are faster you need to determine the surface area of both. But again, all of these forces are highly dependent on conditions. Higher surface area will generate more suction force which is not necessarily proportional to the increase in friction force.
My advice: Just make them the same speed and simplify your life and go ski/board instead.
Credentials:
BS Mechanical Engineering
MS Electrical Engineering
PhD Materials Science & Engineering (in progress)
