My wife and I also have had the opportunity to dive both places. Wow, hard to pick one over the other, however, if you are going to GBR, don't pick end of June-early July. As you are aware, that is their winter, and we had some winter weather! Strong winds for the whole week, which mucked up the diving somewhat, but made for a lot of rocking between sites. Palau was great, stayed on Ocean Hunter III, would do it again in a heartbeat! Both places we saw sharks nearly every dive, it was a rare dive we didn't have sharks. GBR got to hang out with Dwarf Minke Whales, which were migrating thru, which is an advantage of going in June-July. Getting to Palau is a "pita", well, Australia is no short ride either. We flew Air New Zealand to Oz, they provided good service, when we went to Palau, Continental was only option. If in Palau, take an afternoon off and go tour Pelilu. Both my wife and I like the easy pace of liveaboards, if going that far to dive, allows you to get a bunch of dives in. If memory serves correctly, we did at least 4-5 dives each day in both Palau and Aus. Take a couple extra days to see Palau, (Palau Pacific Resort is nice place to hang out) obviously more time needed to see Oz!