At Fulham Dempsey had the luxury of being allowed to drift in to the centre from the left wing, this mean't he could quite easily lose his marker (the RB) and find space between the lines. At Spurs he plays between the lines so the Centre backs know to pick him up. So essentially, he's doing the same job but in a more difficult way.
Fulham played a 4321 formation with Dempsey and Duff cutting in and playing off Zamora as a classic target man.
Murphy's long passing made them able to break very quickly. Dempsey isn't quick but he's a really strong runner on the counter attack.
To actually get the best out of him we'd have to play something like;
Lloris
Walker Kaboul Vertonghen Ekotto
Sandro Huddlestone Dembele
Bale Dempsey
Adebayor