I've had both, but only used the 276C on my sled. A bud bought my 176C and uses it on his SRX.
If you've got the cash the 276C is a better unit. The screen is better. The built in Li battery in the 276C can run the dang thing all day if you take care. Backlight off during the day, on low at night, turn it off when going into bars and such. I've been amazed at how well it works even with the cold.
But the 176 does take standard AA's. So where I carry a cig lighter cord on my sled for my GPS "just in case". He can run into a gas station and pick up a 4-pack of batteries if needed.
Trouble? Nope. The 176/276 use Garmin's unique memory card format. The 176 is limited to 128MB, the 276 can take 512MB. For just snowmobiling either is fine.
The 276 really shines in the car, or on my motorcycle
, with it's much better on-road navigation features.
It's more expensive too.
I'd look used. The 376C came out a few months ago and there are probably be people upgrading.
Don't forget that you'll need a GPS, a data card, and the map software. Where some of the other units include this all in a package.