Is this really true for the average Googler? Honest question.
From what I hear from friends working there, superstars like Peter Norvig or Sebastian Thrun may get a year(EDIT or more! see comment below) to work on self driving cars or massive neural networks doing computer vision etc, but a lot of developers just fix production bugs on Gmail or Google Plus or whatever, and implement incremental features decided by their managers and don't really have the option to work on the cutting edge projects, especially if you aren't working in the Mountain View office.
(Not to challenge the rest of your points, they also tell me Google is a good place to work, but Sebastian Thrun might be able to pull off working on self driving cars even at Facebook.)
Fwiw, if I had to select between FB and Google, I'd go with Google (I have some superficial reasons not to work for FB, mainly because I don't want to do 'social networking'), but once in I'd do everything I could to change teams to one of these world changing groups ;).