The two places you're asking about don't have much in common except that they are both very exciting (and expensive) destinations. I like to compare all aspects of a trip, not just the kind of diving they do.
I've done two live-aboards at each destination over the years. I've also dived with Sam's Tours in Palau and did a lot of land tours. Palau has more big stuff and less exciting macro. PNG (depending on where you go) has AMAZING macro with very good big stuff too. Both have great topside attractions, but the PNG highlands is hands-down more exciting than what's in Palau. If you do a live-aboard to either place spend some time on land too. You'll be really sorry if you don't. PNG has more diversity.
In both places there will be dives where you can dive right from the back of the boat or get dropped off and picked up by dingy.
In Palau you'll cover all the best dive spots regardless of what boat you're on, so go for a nicer boat. PNG is more spread out and would take a lot more time to visit all the best spots. I've been to Milne Bay at Tawali and on the Spirit of Niugini and to the south coast of East New Britain island out of Rabaul on the PHD Star Dancer. There are still other areas I want to go to but they will be trips in the future.
Palau is probably a safer place to visit. PNG is more rugged and isn't as glamourous.
Palau smells better. MUCH better.
PNG has WAAAAAY better artifacts and art to buy and take home with you and its much less expensive than what you find in Palau.
If you travel to Palau you only have Continental Micronesia to take you there. Don't even think about the island hopper flights. They are horrible! PNG has more options depending on what day you fly and what country you fly through. Both flights are expensive, but if you do go to PNG, get your ticket from
South Pacific Island Travel. They have tons of experience in both areas but have the best prices on PNG tickets that I have found.
Both are amazing and which ever one you don't pick for this trip, put it high on your list for a future visit.
Hope this helps!