Why not both? Spend 3 or 4 years in AK and do some hunting there. Get a couple of Brownies and Griz, moose and caribou, sheep and goat and then move to Utah. I've been to AK and it's a great state but not easy to get around. And like you said, winters are dark, long and cold. I like it here in MT where there's deer, elk and trout and some places in UT are like that. Wouldn't want to live anywhere near Salt Lake though.
Living a few years in AK would be a great opportunity to hunt a few critters that would cost the rest of us multiple thousands to hunt. It would still be spendy as res to do it there, although not near what it would cost a non-res.
You didn't mention if you were married and if you are, that would be your top prority. But it sounds like you're single which would give you a lot more flexabilpity. You need to figure out your short term and long term priorities.
If I could wind the clock back, I would like to spend about 5 years or so in AK and get my fill of that and then settle permenantly in MT.
Just my tow cents