The Hyatt Regency is the older property with the 'round' towers. Doing a search you'll find lots of comments on this hotel, most pretty negative. On occasion, I've been upgraded to a duplex suite here, and it is a much larger/convention style hotel. The RC is generally closed, in all my stays I've seen it open twice. As a Diamond, you'll get your usual amentiy choice and if the RC is closed a certificiate for breakfast. This hotel is closer to the ORD and if coming by way of the Blue Line, you can get off at Rosemont and walk rather than going to the airport & waiting for their van (which serves both properties).
I do prefer the newer Hyatt Rosemont, which is smaller, and more 'W'-like in decor. It has only one restaurant which is a combo snack bar/bar & casual dining area. I don't know about upgrades to suites here (as I've never received one, nor requested one). But the rooms are nice. It is a bit away from all the other airport hotels and not much else around for dining variety, although I believe there is a steakhouse a block away.
I generally stay at ORD when I have an early am flight after working in the city, so my stays are always just one night.