Gosh, I'd probably say it's really close to a tie between them. Have stayed at both, really like both.
Old Key West is very lovely, is pretty newly refurbished, and the studios have 2 beds, which is a pretty huge plus. The resort itself is very charming, and I always feel "home" when I'm there. The pool area is enjoyable but nothing outstanding either. The boat to Disney Springs is nice, but I'm not entirely sure it's even running at the time. Another con is that food options are pretty limited. Don't get me wrong, the food is good, but just not a lot of variety.
Saratoga Springs will be a bit hit or miss on the "newness" factor. If you spring for the preferred rooms, you should have a nice new room. Now, the non-refurbished rooms....it is still clean, it is still well-appointed don't get me wrong. They do the best they can with what they have. BUT.....the pullout couches are hor.rend.ous. So, if you can do the preferred upgrade, you'd be getting a Murphy Bed, which is a huge upgrade. Transportation-wise it's a winner, especially if you spend a lot of time in Disney Springs. Also, if you want to go to any of the other resorts, it's an easy walk over to the bus station, and you can catch the bus there. The food isn't as good quality as Old Key West, but they have a few different options, and we found the Grill at the Paddock to be pretty good. Plus you are a stone's throw away from a TON of yummy food.
Then there is the experience side of things you mention: like many have and will say, it's really up to you and your family and what kind of vacation you enjoy. OKW to me feels like "old Disney." It feels like a home away from home. There is a sense of peace when I'm there. You feel like you are away from it all. I give OKW the edge by a hair. BUT...there is also something very enjoyable about sitting on the rockers at SSR, on the river, watching boats go by and the comings and going of DS.
Ultimately, I don't think you can go wrong....but from the comfort side of things, I would recommend OKW or the refurbed SSR rooms.