I reckon you will end up doing what the majority of your fellow seasonaires do, or at least at first. Strangely alot of seasonaires board over ski, although skiing becoming much more popular again.
Get a good relationship with the local hire shop and you should be able to swap and change through out the season without too much trouble.
Boards are easier and more fun in crappy off piste conditions (unless you are a very good skier)
Boards v Skis schussing, it all depends on the ability of the boarder/skier and how good they are at keep the skis/board flat. Carver skis are harder to keep running flat therefore can be slower than a board, but at least when you do stop you can still keep going. Modern skis do not let you have the same ability to get to nutty speeds and still do controlled fast turns, unless you get racing skis.
Off Piste - In decent quality snow skis and boards are just as much fun as each other but in different ways. Many people do not truly know how to ski off piste and end up putting far too much effort in to it, ending up knackered where as boards on the face of it require less effort. Learn to ski properly off piste and you can do it on any type of ski effortlesley.
Me - I've skied for 26 years, raced, skied with some amazing boarders and skiers off piste and wouldnt really change to boarding as I find it too much of a faff, but I do like it for a change, and when I fancy a bit more of a challenge.
Some of the best days skiing I've had have been where there has been a mixture of boaders and skiers, and none of this stupid them and us thing. Total respect for telemakers though, wish I had learnt when I was a bit younger !