I liked Fairbanks better. The people seemed more friendly for the most part, and it had all I'd need and more.
Lots of good hunting from there, just about any direction you go.
Anchorage is bigger, with more places to buy outdoor gear, and for the wife to go shopping, but there's still plenty in Fairbanks.
If you're into salt water fishing, then Anchorage would be the obvious choice. It's rivers and lakes around Fairbanks, but plenty of them.
In truth, I'd try to choose North Pole. It's close enough to Fairbanks to almost be considered a part of it, but a little more rural.