I voted Alaska.
Our first cruise was Alaska (our girls were 12 and 16), second cruise was Northern European/Baltic (our girls were 14 and 18.) For us, the itinerary is what is getting us to cruise. We have no interest in the Caribbean, especially in the summer as we don't like the heat, and we're not really 'beach' people...if I want to go to a beach, I can drive 1-2 hrs to go to one. DH really thought our Alaska cruise would be a 1 and done for cruises, but we really enjoyed it and he was willing to do the second one...and now we have a placeholder to try and book a 3rd cruise for summer 2020. As far as Alaska vs. Europe for kids--I'd wait on Europe until the youngest is in middle school--tons of walking, a lot more architecture/history/museum type visits as well as the longer transatlantic flight, and possibly long drives to major cities if you do the Mediterranean. Alaska is great for all ages due to the nature aspect. And...since it's colder, kids will find the heated pool less crowded than Caribbean itineraries. We also loved seeing characters in their Alaska (and European) outfits!