We've been on two Alaskan cruises - one on
DCL (RT out of Seattle) and one on NCL (one way from Vancouver to Seward with an additional week on our own exploring the Kenai Peninsula), one land based trip to Alaska, and the DCL Norway/Iceland/Scotland cruise. All were amazing in their own way.
The way I see it the main differences you will encounter between Alaska and Europe are:
Much, much more potential for wildlife in Alaska - though you will probably have to drop some $$$ for excursions to see a lot
The European cruises are fantastic for experiencing an entirely different culture.
As for scenery, I think it depends on the Alaskan cruise. Unfortunately the DCL itineraries (with the a few exceptions that go to Hubbard Glacier), don't really showcase the best of Alaska in my opinion. The one way cruise we did this summer went to both Glacier Bay and Hubbard Glacier and then allowed us to spend a week in mainland Alaska. We spent 18 days with breath taking scenery throughout the trip. Simply incredible. Every bit as fabulous as our European cruise, and if I really had to choose I'd say Alaska was better.
As far as port towns, I would give the advantage to the European cruises over Alaska. Honestly, I hate to say this, but I think Juneau/Ketchikan/Skagway are kind of tourist traps. Yes, you can take an excursion and get out of town - and you should! - but I thought the port towns in Europe had so much more charm - probably because they were so different than what we see in SW PA

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If you loved Alaska, I think you will love Norway, but I'd definitely recommend looking at the cruises that go to Iceland as well. The scenery is breath taking and the people are incredibly warm and friendly (in their own unique way!). Also, Iceland has some great thermal features, similar to what you will see in Yellowstone. Plus they have these great black sand beaches due to the numerous volcanoes. It's a pretty special place.
Edited to add: Don't discount the Scotland factor of the Iceland cruises. Kirkwall was our second favorite port to Reykjavik (and better than Akureyri). The historical sights are just incredible there.