I'll echo what others have said - Disney service at the non-Disney hotels on Disney property (i.e. the DTD area) is spotty at best. I've heard many horror stories about their transportation - it is NOT run by Disney, like the rest of WDW is.
There are elevators at Pop Century, and the rooms are not huge but I don't find them nearly as small as some people make them out to be. It's really up to you - do you want to spend your time in a big room or at the parks? If it's the parks, then Pop is for you. It's very close to Epcot, MGM, and AK - busses to them take 5-6 minutes or less. MK is a bit further away, but it still offers direct transportation.
You won't get that with the DTD resorts - nor do I believe you can charge back to the room. They also will lack the Disney "magic" that even a value resort like Pop Century has.
It's a no brainer for me - I only stay on Disney owned properties because of all the benefits you are assured (most convincing of which is the transportation). It's up to you to see what works for your family - though I'd suggest going to mousesavers.com and checking on current discount codes - I'm sure you can get a cheaper rate at Pop then you'd get at one of the DTD hotels.
N.E.D.