Thing is, it's like comparing Beckham and Scott Parker. Parker's better these days, but only because Beckham's past it. When comparing them both in their prime Beckham's a higher level.
Cahill in his prime was all over the pitch winning tackles, hassling defences and of course scoring loads of goals. Dempsey's better now like, and has always had better technical ability, but what people seem to have forgotten due to his barren spell is that Cahill used to be one of the best goalscoring midfielders in the league. He was the player that, even over Arteta, all opposition fans would fear most.
Even though they've basically played the same position they're very different. Cahill's always better at what his strengths are, and the same for Dempsey. But if you asked any other Premier League fan who down the years has been better I think they'd say Cahill.