I don't think they are really more talented than the Cowboys. However, I think they can beat the Cowboys even when the Cowboys are better than them. That's the difference.
The Eagles teams have always competed harder in games with the Cowboys. I don't know why, perhaps it's indicative of their fanbase, but they have always possessed a certain malice towards the Cowboys and the Cowboys have never really reciprocated.
It almost always seems as though the December matches between the two are more important to the Eagles, demonstrated by their intensity.
If Cowboys are to defeat the Eagles, they must learn to develop an animosity towards the Eagles, a desire to inflict damage to their momentum and confidence. Until then, all we will see in late season matches is confusion and shock by the Cowboys, an inability to take their game to the level required.