Haven't been skiing at either of those places, but I've got a press kit from Sun Valley with lots of info. Sun Valley was recently voted the #1 resort in North America by Ski magazine readers - out-ranking traditional winners Vail and Whistler/Blackcomb.
In terms of lodging, looks like there's several options. The Sun Valley Lodge has 148 rooms, and the Sun Valley Inn has 113 rooms. There's another 269 rooms at various apartments, condos, and guest cottages.
Winter activities include skiing (2,054 acres with 18 lifts, including 7 high-speed quads, 78 runs, vertical of 3,400 feet), XC skiing, snowshoeing, ice skating, sleigh rides, and two heated circular outdoor pools.
On restaurants (from the resort): "After an indulgent day of shopping guests can relax with a coffee or light meal at the European-style Konditerei, which also serves breakfast and light dinner. The Ram Restaurant specializes in Idaho steaks and prime rib, complete with a weekend buffet; or, for more informal fare, there is Bald Mountain Pizza & Pasta. The Sun Valley Lodge dining room is famous for its more formal dinners and Sunday brunch, while Gretchen's provides a gracious, yet informal mealtime setting. After dinner, head for the Duchin Lounge, a Sun Valley tradition, for drinks, dancing, and entertainment. And, for apres-ski, visit the Boiler Room, where comedian Mike Murphy keeps things moving. The quaint Sun Valley Opera House, also located in Sun Valley Village, shows first-run movies as well as the 1941 "Sun Valley Serenade," with Sonja Henie."
There's lots of shops and restaurants in the nearby town of Ketchum.
I hope this helps a bit. There's tons of details in the press kit and I'd be happy to try answering any specific questions you have.
In terms of Jackson Hole, its known as a definite cowboy town and there's lots of rustic places to eat. I believe a popular side-trip is to go snowmobiling at Yellowstone National Park, which I hear is excellent. The Grand Tetons are very beautiful. The skiing at Jackson Hole is more advanced than your average Colorado resort.