I stay at each about once every two months (in rotation with the other SF Airport Hilton affiliates). The Lounge at the Hilton is very nice and Bay views can be, as well. Other than that, I prefer the Doubletree. (It's also within walking distance of some elements of civilization.)

Parking at the Doubletree is uncovered; your car will absolutely get dirty, that close to the Bay. At the Hilton, it's under the building.

Both properties are served by a shuttle to downtown Burlingame. Neither property is likely to mention this; half the staff has forgotten.