I was onboard the Rock Island Aggressor last month. She was in good repair and well equipped. The catamaran configuration was spacious and all guest areas are on or above the weather deck. Food was outstanding, better than I had during the two weeks ashore. Cabins were clean and comfortable. The crew was helpful, friendly, and knowledgeable.
As near as I can tell, all LOBs dive off smaller tenders (twin outboard open boats with seating and canopies) -- which makes senses given the amount of drift dives and very shallow reef. The stern lifts on the Aggressor boats are really nice compared to transferring on and off a tender floating off the swim step. I was told that the Aggressor boats installed all the moorings at dive sites -- they have hydraulic power packs and drills. As a result, none of the day boats or the Aggressor's need to anchor. I would say about half of the dives on that trip were live-boating.
For the most part, all the day boats dive the same locations and off very similar boats. The big difference is very few day boats are there for your first and last dives of the day (too early or late for them). It can be a real mob scene on most midday dives due to the large number of boats -- off a LOB or dayboat.
All diving operations that I saw in Palau are pretty strictly guided (hearded), which is not something I enjoy. I understand why, but I don't like it. In that way it isn't much different than any other recreational diving area in the tropics worldwide except for some operators in Truk or hiring a private boat.