My friend Chip who snowboards was asking me this same question a couple months ago, this is the response I wrote to him.
Both have their pros and cons. I personally use my Contour for skiing stuff. They are much lower profile and the side mount (on helmet or goggle strap) is really much better designed than GoPros clumsy top of helmet mount. GoPro does make a great chest mount but for snowboarding it would be kind of silly, great for skiing or mtn biking though.
In my opinion Contour has more flexibility with adjusting exposure (so that the image isnt too overexposed by the sun or blown out aka too much white).
Many people tend to think that GoPro offers slightly better quality than Contour. I think the edge is very minimal and not noticeable to most people. I own both, for shooting fishing or random fun videos I use a GoPro, for skiing I strictly use my Contour. Both are very good cameras though and you will be happy with either. Both have a large variety of mounting options. I love how Contour has mounts for either your Goggles or helmet and they have multiple helmet mounting options (the side profile mount is my favorite).
GoPro:
Pros -
+ Slight quality edge (barely noticeable)
+ Can take still photos in one mode (not amazing quality but still good)
+ Larger company, accessories are easier to find in store
+ Better for hand held fun, random videos (weighs a bit more so its more stable, also a con if you are riding though)
+ Waterproof case included (fun for vacation videos-ie. swimming and underwater shots)
Cons -
+ This is a BIG con for me--VERY bulky/clumsy when helmet mounted (you just look super goofy with it helmet mounted) - See Photo:
http://www.racerxcanada.com/images/news/new-products/2008-03-19_gopro/08-03-19_gopro-two.jpg
+ No manual adjustment of exposure (easier to have an overexposed or blown out image)
Contour:
Pros -
+ Much thinner profile, great for skiing/boarding - See Photo:
http://helmetcameracentral.com/images/ContourHD_helmet.jpg
+ Probably cheaper, they have worse marketing than GoPro so they are desperate for sales.
+ Smaller company (most likely easier to deal with, more desperate to please customers)
+ Can adjust the exposure and audio level manually with Contour Storyteller on your computer
+ Lighter
Cons -
+ Perhaps slightly worse quality
+ Heavy with Waterproof case (but waterproof case is NOT necessary for skiing, trust me, I've used it without the case in blizzards before).