I'll chime in with a few more Hyatt positives. (I really can't think of any way that GP is inferior to Hilton aside from breadth of properties)
+ It's interesting that Hyatt has a MyWay-like program for Diamonds. The big difference is though that Hyatt Diamonds get all 3 MyWay benefits - lounge access, breakfast (every day of the week), internet, and 1,000 points (and, 1000 GP points are a lot more valuable than 1000 HH points)
+ Far better property-specific G bonuses which are good on every rate. True, they don't always post, but an email to GP takes care of it. And, the G bonuses can really add up - my $63 Hyatt stay tomorrow night has a 2000 point bonus associated with it
+ Pretty good mileage bonuses - HH had the bmi promo a few months ago and some mediocre DL promos, but Hyatt has consistently had some great airline bonuses (true, you will need to forgo GP points, but can be a good deal at a $60 Hyatt Place). Right now, I think you can get close to 5 SW RR credits for a 2 night stay, 2.5 for a one night stay. Back in October, it was 6500 UA MP miles for a 1 night stay
+ An elite-friendly culture - I don't think I need to comment on Hilton but Hyatt is really going all out to add in benefits for Diamonds. They just added a 2500 point bonus if the Regency Club is closed - and you still get breakfast
All in all, Hyatt is definitely my preferred program. And Hilton, well, I just don't see the value in continuing to worry about my Diamond status, especially when it's pretty easy to get Gold and the benefit differences are minimal...