Obviously, both work. You can find an abundance of examples of each. But which one should you do? I think it depends on your background. If you are solid at either one, do that. Just like in the downhill environment they each have advantages and that is what I am going to quickly look at.
I think the advantage here would be body position. Riding heelside puts you in a position to face the kite. You don’t have to twist to put both hands on the bar and your harness is facing the kite. This puts you in a relaxed position and allows the harness to do what it was designed to do in a comfortable way. The board does have the disadvantage when you need to get move around without the kite’s power moving you. Just like in the downhill world, if you need to cross flat ground or go uphill for any distance it is difficult to do strapped in.
You can walk in skis without taking them off. If you are out of position or even when you are setting up your gear in deep snow, you can easily get around with the skis on. The disadvantage is you’re body is always a little twisted. To edge your skis they have to be perpendicular to the kite lines and your hips will be following your skis. This means the harness will likely be more closed to the lines than you would be on a board. That means the pull on the harness will be greater on one side. Not a big problem but not quite as comfortable as riding heelside on the board where your hips are more open to the lines and the pull. Also, not a big deal but you have to reach across your body with the upwind arm to two-hand the bar.
So which is better? Whichever you like better. The point here is to talk about the difference in case you are on the fence as to which you want to start with.