Pembina, I have stayed at Huracan five times (soon six), and Turneffe IR three times... Both are awesome. TIR is certainly more "upscale" and has a more "resorty" feel in that it has a pool, bar, and is quite a bit bigger and perhaps takes 30 - 40 guests, many of whom are there to fish. I have nothing bad to say about TIR, other than I think their bar prices are "punitive"!
Huracan, on the other hand, is more like a B+B. Eight guests max, a help-yourself kitchen and bar (on the honor system). It's more remote, but not at all "roughing it". The rooms at both places are very nice, the food is great at both and the staff is awesome in both places. Huracan is significantly less expensive and in my opinion, the diving is better due to it's proximity to Halfmoon Caye.
Our decision to go to Huracan after being at TIR for several years was driven by the proximity to Halfmoon which we loved diving (even compared to Turneffe) and because we were travelling with a single friend and the single supplement at Huracan was almost nothing.
Privacy is more possible at TIR... places to wander, a private cabana etc where at Huracan, you really are living with the other guests. Having said that, one of the things that we love about both places is the cool people we meet at both places. Most seem to be highly educated and very interesting... literally everyone from a Nobel Peace Price winner in medicine who treated my ear infection at TIR to an actual Rocket Scientist from NASA and her daughter at Huracan! Mercifully, Mrs. Stoo holds a PhD, so she holds up that end in our family, where I am there for my good looks and charm.
As for ITZA, it's a neat looking place, but it's always virtually empty, with perhaps a group of Marine Biology students or something. The Manager of Huracan has told me that the place is about to close (and may have by now). You should also be aware that ITZA does not have it's own dive operation. Those services are provided by Huracan, so even if staying there is an option, you will still be diving with Huracan (which is not a bad thing, but you will be less involved in the dive site planning etc.). If you were to take a group to ITZA, they would charter their own boat and DM and get fills at Huracan.
As an aside, both of the Belize Liveaboards spend the majority of their itineraries out around Long Caye and Halfmoon, and some around Turneffe. You can't go wrong with either location.
As for diving the Blue Hole, this is where Huracan shines. Being only about 12 - 15 minutes away, we are finished our dives before the other boats, including the one from TIR are just arriving. The GBH is a fun dive, but I hate doing it when there is a lot of other people around. 99% of them appear to way beyond their comfort levels and that kinda freeks me out.
I hope this helps... Feel free to PM or post any other questions and I will answer as best I can.