SSR is newer and shinier. The furnishings are more upscale. Old Key West feels very "Florida-y" to me with pastel walls, lush landscaping, beach-themed artwork in the rooms. Saratoga has covered hallways that run the lengths of the buildings and the doors open off them. OKW also has doors that open to the outside but they are not covered. OKW only has elevators in a few buildings added later. If you can't climb you will have to request ground floor (which will be granted). Saratoga has elevators in all the buildings.
The locations are very similar. The properties are practically adjacent but Saratoga is closer to Downtown Disney. Saratoga has a sit-down restaurant and a gift shop with adjacent counter food place. It has a main pool near the check-in and some quiet pools further out. Old Key West has Olivia's restaurant which serves all 3 meals, plus a gift shop with some food items plus a snack bar at the main pool and a part-time one at the Turtle Pond (quiet) pool. The main pools at each resort now have slides and therefore lifeguards.
At OKW you can park right in front of your building. The patio out back will have a small table and view of the grounds. At Saratoga you might get a view of the grounds or water or even Downtown Disney but I think you might also see parking lot. At each resort the buses can take you directly to the parks or you can hop a bus to get around within the resort itself -- both of these places are BIG.
My family LOVES Old Key West. We love the feel and the colors and all the flowers. We love the people too -- it is full of friendly folks. While we haven't stayed at Saratoga yet, we toured the model center last trip and were quite impressed with how lovely it looks now that it is practically done. I think your family would enjoy either and I recommend you go to AllEarsnet.com and look at the slide show of each resort, choosing the one which gives you that WOW! They are both beautiful resorts with lots to like, and I think you will have a ball no matter which you choose. Beware -- this great "bargain" rate may cost you a fortune as you will want to buy DVC!
Have fun!