The experience may by $2000 more, but personally, I think the second week is way more fun than the first. It's double the fun, so in fun dollars it'll only cost half as much.
If you're staying on-site, it's the second week that will completely remove you from the reality of this troubled world, replacing it with a Disney version. Disney version of reality is the best ride off all. You can pace yourself, go back to your favorite rides, get more time in at the resort pool (and by they way Disney resort pools are terrific), and be able to spend time looking at WDW close up... You know people rush too quickly through the parks, without taking the time to look at the incredible detail that Disney has put into their version of reality.
Honestly, we booked a 1 week trip to WDW, that was supposed to then be followed by a sightseeing drive... well that plan got tossed on day 6, and we ended up with as 12 day Disney dream vacation... We started out with a 1 day extension... then 2 more, then 1 more.... all the while we were being enticed by the hotel front desk, who kept leaving offers of a discounted room rate if we'd stay just one more day.
Whatever you decide, you're going to have a fantastic time...