I have a Contour GPS, love it.
Before buying it I looked at a few video comparison of the GoPro Hero, Contour 1080, and Replay. I was not impressed by the quality and framerate of the replay quite a bit when compared to the two others.
The GoPro Hero and Contour 1080 seemed to be pretty comparable, each with their respective strength and weakness. I'm not sure about the Hero2, as it was not released when I checked.
I tend to prefer the Contour, especially the GPS and Contour+ version for their ability to pair to a Android Device or iPhone through bluetooth to allow setting modifications on the field, and "streaming" the video to the device to align your shot and set the white balance and what not according to the actual weather conditions.
The Contour as a slimmer profile and is more suitable for airsofting I think, especially when mounted on an helmet with ARC rails or Contour's side mount, or on a gun (I can't imagine how a GoPro would look and be annoying mounted on a picatinny rail...!)
The GoPro have a bit more accessories available and are a bit easier to get, but whatever Contour offer will suit most needs I think. Buying accessories online will save you a few bucks anyways, so that make them easily obtainable as well :P
Contour had some pretty sick deal in the past few months to try to outsell GoPro (I guess) which is more popular, being on the market for longer, etc etc.
Your call really, it'll all boil down to personal preference in the end. The GPS function of the Contour GPS is pretty neat as well
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Edit to better answer OP's specific questions regarding mounts:
IF you have a helmet, the best way to mount the GoPro would be on the VAS shroud as they make a mount specifically for that
The Contour has side mount you can stick to your helmet if you don't have ARC rails. If you have ARC rails, the best mount would be OPS-Core custom mount, specifically made to mount a Contour on the ARC. That's what I use, it's very stiff and nice.
I tried the goggle strap mount; Didn't quite like it as the Cam's weight had me tighten the strap to it's max (leading to a headache, but I'm particularly prone to headaches) and it was still wobbling a bit but acceptable.
Contour also has a picatinny mount, so mounting to a gun is painless and quick. It's size even allow to mount it on a handgun, if the rail and barrel length is long enough (HAven't tried it on my HiCapa 4.3, but I'm almost sure it'd fit.
Take a look at the official mounting options on Contour's site:
http://contour.com/products/accessories
haven't checked GoPro
Hope this help