Having stayed at them both, my opinion is simple: The commons areas of the Courtyard are far superior, but as LisaRay points out, you can "pool hop," or at least you could about two years ago (heck, when were you there, LisaRay? Might have passed right by you).
As for advantages, the Fairfield has a continental breakfast free. The Courtyard has bigger, nicer rooms. If I remember correctly, the Fairfield does not have refrigerators, the Courtyard does (although they're funky little devices, really an electric cooler more than a refrigerator). The balconies at the Courtyard are nice. If I couldn't get one, I'd probably stay at the Fairfield.
The location, regardless of which you choose, is fantastic. As for eating places nearby, I there's several restaurants right outside the compound (two minute walk), one of them a "Lone Star Steak House," which is great. And within the complex is a food court, including Pizza Hut and a TCBY, an Oscar Meyer hot dog shop, and a pretty nice deli. Plenty of food to choose from if you didn't leave site for four or five days.
I think you'll enjoy yourself in either place. But if you give up the free breakfast and pay the extra for the Courtyard, get a balcony.
Pat