Alaskan cruises are great, but can be a bit of a hassle, depending on where you are from. If you are on the west coast, it isn't too bad, but if you are on the east coast, you often end up having to change planes 3 times, and it takes a really long time to get there. You also have to do a lot of pre-planning if you plan to do land tours separate from the ship tours. On the other hand, there is nothing like being 4 hours into Denali; that's some wilderness for you. We hiked Matanuska glacier, played with sled dog puppies at the Iditarod museum, and then took the glass-topped train fro Anchorage to Seward to catch the ship.
The thing with cruises to keep in mind is that most people on them aren't looking for strenuous hikes and wilderness. They want to see something cool, and hang out on the beach. We like snorkeling, so we tend to do Caribbean cruises. We also did a MEditerannean cruise, and I can't stress how amazing that was. In the US, something is old if it's 200 years old. That's remodeling in the Mediterranean. Walking on the street where Cleopatra walked is walking on some serious history.
Given the choice between RCL and NCL, I would definitely go with RCL. Granted, you have no frame of reference, but I've been on both and RCL was just better all around. Personally, we like Celebrity; peter food, fewer kids. My kids preferred Celebrity when they were young, as they are foodies too. We have also done Carnival, and it wasn't awful, bu ti'd not do it again.
I wouldn't do a cruise out of Asia. I'm to going to go into why as I would come across as xenophobic, but people I know who have done them say it was pretty bad.