First off, I just want to acknowledge that this is pretty subjective and one diver's best-dive-ever is another's if-I-ever-get-my-hands-on-that-travel-agent... eyebrow. Also, there may be circumstantial (sp?) differences; for example, I happened to see bull sharks in Fiji but I could have seen (but didn't) tiger sharks in Palau.
In Fiji, I saw a more diverse array of fish and they were, to some degree, fish that got me more excited. I saw more nudibranchs (and a better variety), blue ribbon eels, prettier coral, lionfish, lots of various types of shrimp, and an octopus. I did see some sharks in Fiji (including some bulls) and a wreck so I, at least, addressed some of those interests. When I was there, the vis was better in Fiji (August) than it was in Palau (December). There was also more variation of dive type in Fiji (some drift, some wreck, some concentrating on small but densely packed bommies) than in Palau (almost exclusively drift -- I admit that I could have taken a more active role directing this but I tend to trust divemasters regarding a region's best dives). Additionally, at Beqa Lagoon, there was unlimited free shore diving. On top of all this, the food and Beqa Lagoon was better than what we found in Palau. Finally, we were able to get a 10 hour direct flight from LA for around $900 versus the 24 hour, 4-hop, $1700 flights to Palau (the cost difference is probably at least somewhat due to when we went to both places).
In favor of Palau, however, there were sharks on every dive (and sometimes, quite a few), better drift dives, turtles, better (WWII !) wrecks, and more beautiful views top-side. We also saw some interesting behaviours like a bulldozer shrimp and his companion goby.
I guess my point is not the Palau was bad (it was really cool); it's just that, for my family and me, Fiji was just that much better.