I can't comment on Hyatt lounges, but I've been able to hit quite a few Sheraton lounges in NA. And while I'm sure there are specific instances (possibly like the one you bring up) where the Sheraton lounge is better, that is NOT the norm per my experience.

I'll almost always take the Marriott lounge over the Starwood one. That doesn't mean Starwood doesn't do other things better than Marriott, but at least with lounges, my experience has been much better with Marriott.