I've stayed at both now and if you can do a few nights at both places I would suggest splitting your stay if you've never been. The resorts are sort of the opposite right now. Park Hyatt (Awesome rooms, pools and views, but disorganized service and limited activities) vs. Four Seasons (Old rooms and pool, much more organized service and activities, golf course). You go to the Park Hyatt for the hard product and put up with the poor soft product. You go to the Four Seasons for the soft product and put up with the poor hard product. I've heard the 4S has done some room renovations, but when I was there a few years ago the rooms were in bad shape and it was super $$ back then. I think we paid $800+/night and I remember being very disappointed in the room but enjoying everything else. We did not transfer between the islands this time, but we saw several people doing this so it must be pretty easy and we were told the boat ride was very quick.

If you like to get out and explore and usually have the hotel set up activities, outside dinners, etc. you will like the 4S better. If you like to stay mostly at the resort, enjoy more modern hotels, put a premium on ocean views, etc. you will likely prefer the Park Hyatt. We have young kids now, so typically don't venture out as much as we used to, so the Park Hyatt was perfect for us, but we did miss the quality service and better organization of the Four Seasons.