We did HAL before we had kids. Several things:
1) Alaska cruises are really some of the absolute best for cruising!!! (We've done both
DCL and HAL.) You simply have to go!
2) Don't pick the first cruise of the season - it may be cheaper, but they haven't gotten the ship put together really for the itinerary and regardless of how many times they've sailed it, there will be hiccups. Plus most of the really cool excursions are simply not available yet in the season.
3) Pick an inside passage cruise - PARTICULARLY if you get seasick. That outside passage can be a real doozy! (And make sure it's inside both ways!)
4) If you can, don't book a round-trip cruise (unless you can stay out for 14 days or so). The best thing we did after our HAL cruise, was get off and take the train up to Denali! The views are spectacular and the wildlife amazing! (Unfortunately, you can't do this with DCL.)
5) Do note though that HAL's demographic is very different than DCL. Although I think it's probably slighly younger than Princess. We didn't have kids yet on our cruise, but there definitely weren't very many families on our trip! That said, I think HAL did the nature experts better than DCL - again catering to the demographic.
6) If you go after June - take mosquito repellent! Some of those things are bigger than birds!
7) If you can afford it, the balcony cabin is the way to go. Up on deck it is REALLY cold on that glacier day!
8) MUST go whale watching!!!! Must take a seaplane!!! Dogsledding is COOOOOLDDDD and often cancelled. Eat some fresh salmon too! (Can't stand the stuff down here - but up there, it's like CANDY!)
Whichever one you choose - it will be truly the vacation of a lifetime!
Enjoy!