I'll vote for the Aggressor too. LCBR is nice, but their approach to experienced divers is conservative. You'll have more freedom to do your own thing (as opposed to trailing around after a DM) on the liveaboard.
Agree on the conservatism for experienced divers. Things were pretty "forgiving" until around 2 years ago...a spat of local diver deaths (across a couple of dive operators, IIRC) very naturally prompted some tightening up, particularly for solo diving.
In any event, 'freedom' is a multi-dimensional question.
A big part of the reason why I personally like places like the Sister Islands so much is the freedom to go for a walk/bike/drive and get away from everyone/everything.
As such, I don't particulary relish being "restricted" to being onboard a boat for a week, as it precludes having time "away" from the boat for land-based options of going for a hike, spending some time at the ponds for birdwatching, a quiet evening walk on a beach, poking around in tidepools, taking in a sunset at Salt Rocks, etc. OTOH, if Lenny Nickerman still has his kayak that I could (ahem!) borrow for some DIY shore excursions...
...Check their website and see how many times they have made it over to Little Cayman in October and make your decision based on that. You can't go wrong with either choice.
Good advice. No week is ever going to be risk-free for making the crossing over from Grand Cayman, but October will be IMO better than "winter" (Dec-Feb being generally the worst). What I've found over the past 20 years to be the common prevailing Cayman weather in the Sept/October timeframe is that one can have easterlies (ENE) that can blow fairly stiff "Down the Slot" for a couple of days, then it quiets down, etc.
Just to add to my post, you can do your own thing when diving at LCBR except for the time allowed that is. On the first two dives of the day we had a 60 minute time limit and then another 60 minute time limit for the afternoon dive. For me, an hour on a dive is plenty. Also, you didn't have to follow a DM around at all. You can if you want or you can go off and do your own thing. They have no problem at all with that.
These bottom time schedule limitations do get accentuated some in Little Cayman, due to BBMP's typical topologies, which often has some nice reef areas where one can drift around in for 25-30 minutes at <20fsw to degass and burn off only ~800psi. As such, an hour's BT really isn't necessarily all too hard when you spend half the dive so shallow.
And while a "First In, Last Out" (FILO) strategy can add 10-15 minutes, its not possible for everyone to use a "FILO" strategy. It doesn't help that it is human nature for many people to rush to be first in even if their relatively higher SAC also means that they'll also be 'First Up', and then end up cooling their heels for a half hour and give dirty looks to the mellow greybeard who was forced to go in last and does his 'allowed' 60 minutes.
Not really sure that this is something that any DM has really ever come up with a brief Politically Correct statement to make in a dive briefing to encourage the proverbial air hog Type A's to reconsider jumping in first which won't potentially hurt the DIve OP's customer satisfaction or staff tips.
-hh
PS: I just got a newsworthy phone call ... Reef Divers on the Brac is now operating.
