I see this thread is a little old-- are you still planning to move to AK in October 2020? If so, I'm not the best source of info, but I'll tell you what I know!
I've worked the last year at a rural critical access ER in the bush, and I'm starting a job at Providence Anchorage in about a month. What I know about each hospital is from an outsider perspective, but here it goes!
1) Providence: the only Level 1 trauma hospital in the state, about 400 beds. Because it's the only Level 1, almost all of our patient transfers go there. If someone has a medical emergency in the bush, we stabilize them, then life flight them to Providence-- unless they are a Native and are not extremely ill or injured. Then we fly them to Alaska Native. Therefore, at Prov you will have the highest patient acuity, and I believe also specialized ICUs. Whenever I've spoken to them in report, they have been excellent, and they have a good reputation. As far as pay, Google "PAMC Collective Bargaining Agreement", and scroll down to almost the last page. There you will find the salary scale by experience. They are reported to be the best paying hospital in Anchorage, but I don't know if that's true or not.
2) Alaska Regional
An HCA hospital-- and the one I hear the least about! Probably because PAMC and ANMC are the two main hospitals we transfer to. I think it's about 100-200 beds, and would assume lower acuity, as all the very critical or difficult cases end up at PAMC. Probably lower stress, but also fewer learning opportunities.
3) Alaska Native
Beautiful inside! There are cultural exhibits all through the hospital! As the name implies, it serves only Native patients. Because of this, as I hear from an ER nurse who works there (staff are all races), it is an interesting cultural opportunity, but hard to always see a lot of the rampant issues, especially surrounding drug/alcohol/sexual abuse. The staff is very unified, I hear, and I've also been told it may be a little slower pace than some hospitals. The most critical cases, or high level trauma, still go to Providence.
I've heard from a nurse that has worked at all of them, that they are all pretty good and there's not one to avoid. I hope that helped a little! Good luck!!