Hi Cruiser 914, and welcome to cruise-chat.com!
I've been on Norwegian Dream (sort of.. see below), Zenith, and Constellation's sister ship Infinity, and am happy to offer comparisons.
I'll get the easy part out of the way first. There are few similarities between Celebrity's M-class ships and N. Dream as far as the ships themselves, mainly due to the sizes of the ships and the onboard amenities. For example, the M-class ships have that marvelous T-pool area, which N. Dream does not.
Zenith and N. Dream are a little closer ship-wise as they were built around the same time and are/were about the same size. Zenith was more elegant, though, as is the case with Celebrity all-around. That does not mean, however that NCL offers a substandard product. On the contrary, we've found it's a good product for the $. Of course, there are other differences, such as Freestyle Dining and a more casual atmosphere. Zenith also had a much larger buffet area than N. Dream.
Now, for what N. Dream does
have. First, her cabins are great, particularly for families. We've had an obstructed view cabin, and it had a wonderful sitting area that included a loveseat that converted to a bed. She also has a good amount of outdoor space, both on the upper deck amidships, and on several decks aft. Show lounge is not as striking as the one on Zenith, but it works.
Her restaurants, particularly the two located aft, are spectacular and offer great views.
But, it sounds like your decision isn't between Celebrity and NCL, but between N. Dream and N. Dawn. In all fairness, we were on N. Dream years ago, before she was stretched. And, we haven't been on N. Dawn. Yet, I would also select N. Dream for the itinerary, which a cruise to Bermuda is really about, anyway. Going through the Town Cut is amazing...something your colleagues and families will remember.
We will be returning to N. Dream in May. Should you decide to book, I can find out more specifics for you. I understand she is to have a cosmetic refurbishment prior to the Bermuda season (new carpets, things like that).
Any questions, please ask!