I've done both....the Juliet and Blackbeard's boats dive pretty much the same sites. A few differences:
Juliet leaves out of Miami, so air fare is cheaper, but you make a night crossing and that can be rough.
12 divers on the Juliet vs. up to 22 on Morning Star, Pirates Lady etc.
If raining, you don't have to go topside to get to the galley to eat on the Juliet.
I had a blast on both and will do both again. I loved the Morning Star and the crew, and the Juliet's crew are excellent also.
The food was quite a bit better on the Juliet but I'm not a picky eater, so the food on Blackbeard's was fine.
104' boat Juliet vs. 65' Morning Star.
Juliet is booked pretty much solid for the next couple of years so you have to schedule through who ever has rented the boat for the week that you want to go if they have spaces available.
Juliet has nitrox.
Those are the differences that come to mind.