Well, the boats aren't exactly the same size:
Nai'a: 120 ft, 30 foot beam, 240 ton displacement, 12 crew
Island Dancer II: 101 ft, 22 ft beam, no displacement or draft given, 5 crew.
Granted a motor sail setup loses some space both on deck and below due to the mast structure, but 20 feet longer by nearly 10 wider makes for a considerable difference in interior volume. And I can't tell as I didn't find layouts for the Hughes boat, but looks like the Nai'a has an additional deck for crew/captain/wheelhouse. So the guest count difference might not be as noticable as the raw number would indicate.
I've been on neither but admit I've been eyeing the Nai'a myself for a future trip. Only suggestion I'd have is to read trip reports if you can find them from people who've been on one or the other, and see how their comments (complaints or compliments) mesh with what your desires are. That and look for layout photos.
Having been on the Juliet in the Mona Passage (off Puerto Rico) which is a 3-masted, 106' boat that took 12 passengers (5 crew), I'd have to say the dive deck area wasn't remotely crowded and cabins were cramped, but sufficient. If I had any complaint at all about them (and this is petty, which means I was quite satisfied) it was that I wish they had a lower, wider rinse bucket vs. the typical Rubbermaid 'trash can' size, and that the smaller oval hatches in the belowdeck hallway were a bit tight to wriggle thru while carrying a rig with strobes on arms (I'm 6' 1.5", running 240ish lbs).
The other 2 liveaboards I've done (TX Flower Gardens) are the Spree, which takes 24 divers, and the Fling, which takes 32, (both excluding any shop divemasters). Those dive decks can definitely feel pretty crowded, and 'cabins' are really just enough room to stand and change between 4 bunks. i.e. Spartan!! But just fine if you're after 2-3 days of dive/sleep/eat and don't ever have time to consider how tight things can be. 