I would go with Guam only because I am an island girl. If you are used to long road trips this is not the one to pick. Beautiful beaches, rich culture, wonderful food, island entertainment~ luau style, hospitality, SpaceA flights to other pacific regions, warm weather all year round and a little hot in summertime, or to be blunt hot and humid~ this would describe Guam. There are classes your children could get involved with in learning the legends of the island and ancient dances, if your into that stuff. When you see something you want at the PX/BX or Commissary, you should grab it or put it on layaway because it may be a while til you see it again. Lots of shopping online.
Alaska: I can only speak on Elmondorf and my experience passing through SpaceA with a 12 hour layover. We got there around 9-ish and the sun was bright and shining, with a small breeze and it was quite chilly-FOR ME but then again I am tropical. I put on my sunglasses and off to the Burger King drive through. Customer Service was average-same as the states. I tried to order breakfast and instead of EXPLAINING why breakfast wasn't being served, she was a little short with her answers warranting me to ask more and more questions. Come to find out, it was 9 in the evening!! The sun did not let up til about 2:30am and it set for only about 2 hours and then it was bright and sunny again right before 5am. The military families are very nice. One lady talked to me about the way of living out there and she's used to the sun all day long. They just deal with it by putting up dark/heavy curtains, some foil their windows and with kids, they just watch the clock and have regular bedtimes by shutting everything to darken the house and go on with routine as if its dark out. My understanding is that during the winter, it flips the other way where its dark for majority of the day with very few hours of sunlight.
I hope I've helped you out a bit, but please do more reasearch on both as this was my experience with Guam and Alaska. I've lived in Okinawa, Japan, for 3 years now and don't mind being stuck on a small island with such nice people. Good Luck!!