Looking at this topic question from an opponents perspective I'd have to speculate that a calculating fan would hope that the team you feel most threatened by should be the team you would hope is unsuccessful.
On the other hand, the homer fan would understand the Logic of the calculating fan, but would root for one team or the other to lose
The typical opponent fan while hating one team or the other would go with their emotions in hopes that their least favorite team wins.
Now according to the concept that the Eagles was a basement team in 2005; Hence, they will end up in the basement in 2006 ...the Giants will be victorious. I'm reminded so often of posters from various fandoms, who profess that the proverbial window has closed for Eagles, and that the injuries the Eagles incurred in 2005 had totally nothing to do with their 2005 standings in the NFC-East. Perhaps they were right ...perhaps not!
Oh the Giants are more than capable of winning this game (we all know the expression - On any given ...yada-yada). But the 2006 Eagles will come to contend on a higher level than in 2005!
So root for whoever you want ...it won't make a difference In the outcome of the game!