Had a unique opportunity to compare the Sheraton Skyline at London Heathrow with the Heathrow Airport Hilton, with multiple-night stays at both on the same trip. (I paid the same rate at both.)

Sheraton Skyline featured:

Quick check-in, 2 free daily newspaper coupons per night, convenient car park, prompt room service with probably the best pizza I've had in London, comfortable U.S.-size room, no charge for my long modem calls to CompuServe (not sure why), service in Sports Bar could have been better.
Also, once you learn the local bus routes, you can get to London quicker & cheaper than by going back into the airport. (All this without getting upgraded off my Starwood Gold, a minor disappointment)

Airport Hilton featured:

A VERY long walk from the terminal (4), even though it's "attached", a check-in queue, VERY high phone charges, terrible renovation noise, overpriced and mediocre food, very high mini-bar prices. Decent room with good air-conditioning, excellent bell staff.