To me there is one difference that trumps all of the others.

Like most here, I don't need a suite when I travel alone but I CRAVE one when I'm on a vacation with my wife. So here are your two options (and please note that I'm Starwood Platinum and Hyatt Diamond):

1. Get four GUARANTEED suite upgrades each year, or

2. Check in the the Starwood hotel, but check the internet before you do to see if they are still selling suites. See what you get. If you know suites are available and they didn't give you one, tell the front desk you are aware of it and ask/demand/beg for the upgrade. If they refuse, call the Platinum Concierge. Finally get the keys to the suite and oh, by the way, once you're there, don't forget to pay for breakfast and internet!

Now there is also a big difference in favor of Starwood. Starwood is supposed to give you the upgrade to a suite even if you are on a Rewards stay. Some Hyatts will, most won't.

If I'm paying for the vacation trip and I have a choice, there's no question that I'm going to a Hyatt (Park Hyatt if available!).