@Dogbowl, I have done solo trips and I have done group trips. IMHO there are advantages to both.
Solo Trip:
Advantages:
Not held to anybody else's schedule or timetable. You can eat when you want, and pretty much do anything you want when you want as long as you are ready to get on the boat when the dive op wants you to. There is a lot of freedom when traveling solo.
Disadvantages:
If you are a social person, and are traveling alone then at the end of the day you have nobody that you know that you can talk about the day with.
If you are traveling alone/solo, you will likely get paired up with an "insta-buddy" who you may or may not find compatible.
Group Trip:
Advantages:
You are traveling with people you know. This means that you will know who is friendly and who might need a "little more personal space".
You will have a feeling for the other group members' diving style and may be able to find a buddy that is a good fit for you.
After the day's diving is done, a "family style" dinner with the group can be a lot of fun and a great way to talk about what you saw today and what you are hoping the next day (or two) brings. It can also be a good time to do a little good natured "ribbing" of others in the group. (In the group I travel with, you can tell how well you fit in by how much crap gets thrown at you. If they like you, it can be pretty brutal at times, but if they don't like you, then they will simply smile and say "hello" when they see you.)
Even if you don't know the other people on a group trip, there will often be a "Meet & Greet" at the LDS before the trip. This is a good time to introduce yourself & get to know people and find out if any of you are on the same flights. (I recently did a trip to Grand Turk and flew out of YYZ. I had friends who flew out of Philly. We were all on the same flight from Charlotte to Provo.) This Meet & Greet is also a good opportunity to talk to others and to "pick their brain" to see if they have any advice or tips prior to the trip.
Disadvantages:
There is always the possibility that someone in the group might just grate you the wrong way. Since everybody knows each other, this creates an additional complication if multiple personalities become involved.
It can always be difficult traveling with a (new) group the first time, and it is much easier if you know at least one person in the group prior to the trip. It can be intimidating to try to break into a group where everybody already knows each other. Don't let this scare you off though, because we have all been that person making their first trip with the group. Don't forget that you already have something in common with them. You both dive.
As for me ... I prefer to travel as a part of a group. I personally find it much more fun. In fact, my ideal dive trip is a group doing a LOB trip organized by the LDS. YMMV.