It depends on your personal taste for styling, because both are very different. I like the looks of the Edge... from somebody else's driveway. I'm not sure that I would want to personally own it because of its looks. The Edge Sport, which I saw for the first time in person cruising through town with a dealer plate on, is probably the trim I'd get. The wheels are huge and shiny, so it just looks cool. There might also be some interior upgrades. It can pull a light trailer though and it still gets 24 mpg with available all wheel drive.
The Escape is a vehicle that can be closer tailored to one's needs. You can get a 4 cylinder or 6, front wheel or four wheel drive (and the Mercury Mariner has available all wheel), and you can mix and match those. If you got a front wheel, 4 cylinder Escape (not sure if this is with automatic or manual transmission) it is rated for 28 mpg which is easily stretchable to 30+ if you are an efficient driver. The Escape can also pull a small trailer.
Don't just use either of these opinions to make your decision though. Test drive an Edge, and test drive a 4 cylinder Escape and a 6 cylinder Escape to see if you think you need/want the extra power of the 6. Also, make sure that the car that you get has Microsoft's SYNC, which is a really neat system for your phone and iPod.
Good choice of vehicles though, and thanks for choosing American vehicles instead of the mainstream Japanese cars.