I just got back from WDW with 3 nights at the Doubletree and 8 nights at the Contemporary.
Here is my take:
The Double tree is great. Price is excellent, plus lots of room. I think 2 adults can sleep on the sofabed. Having the little kitchen was great. We bought food stuff from COSTO and heated up. Very nice pool w/ towels. Hotel staff excellent. I did not try the resturant. We stay here as we like to shop in Downtown visit Orlando attractions/shopping, go to Cocoa beach and the Water parks. I don't want to spend Disney Resort prices to do these things.
The Contemporary is great also. I just plain like it there. I like walking to the MK. I like the EMH. Love watching fireworks from the CR. We were on the dining plan so eating in the room was not an issue. Compared to the Doubletree though the drawer and closet space is lacking, but we managed. (family of 4) I like the pool being near the lake, the slide is a plus. So when I stay here and pay $$$$ compared to the Doubletree I use it as more of a resort to relax.
Hope this sums it up the off-site vs on-site reasons. Both options are good and sometimes if you can do both you get the best of both worlds.