Our favorite ship is the Voyager, however, we enjoy the intimacy of the Navigator as well. The Mariner, while beautiful, has much smaller suites than her sister ships.
We did the Alaska cruise this year in May so there were no children on board. Being such a port intensive cruise, I don't think it would bother me to lose the two dining venues (and, it is only a 7 night cruise). On the other hand, the Mariner has very large public areas while the Navigator does not. In June, July and August, there can be over 100 children on the Alaska cruises -- I cannot imagine this on the Navigator.
In terms of the coffee bar. . . this is the one area of the Mariner that I really disliked. It was very crowded and noisy. Alot of the noise was coming from the staff banging pots and pans while preparing drinks. This area was also used for board games. It is set up well for this..... until the people get over zealous and start screaming when something happens in the game that they like or dislike. This area is adjacent to the library -- and is near the computer area -- not great planning.
In spite of all of the above, I wouldn't hesitate to do the Alaska itinerary on the Navigator -- in May or September only.