Surfing is my main summer activity.
All these other sports are derivatives of surfing so yes I would say that it does compliment snowboarding. But it kind of depends on your riding style, if your a strict park-rat then it probably won't be that similar. But if you enjoy carving through powder and throwing spray off the side of the run, Or if you like to cruise through the pipe, carving up the walls and pulling "floaters" on the lip then it will feel real good to be out in the water surfing.
The big difference I think is how short your ride is, 10 seconds maybe. Whereas with snowboarding you got a wide set of time options. But on the flipside, it makes you really value your time on the wave. On the flipside again, because your ride is so short, its kinda hard to progress unless you catch alootta waves.
I think its harder than snowboarding because you need upper body (back/tris/bis) muscles to really get out, specially on bigger days. Duck diving is kinda of a bitch to learn, I'm not very good at it, but it helps with paddling out.
Also, you gotta learn how to read waves, when its curling right, when to start paddling. Timing is key.
Honestly, paddling is 80% or more of surfing, if you can't paddle, you will have some real problems with surfing
As far as riding is concerned, balance is totally different than snowboarding so don't get discouraged, it might take awhile for you to actually have a good time out there. But, once you get in the zone, its well worth it.
I advise you start out on a soft-top longboard because it paddles faster and you'll be able to get up a whole lot easier.