This camera not only has a nicer body and more features than the F550EXR, but it also has faster start up and shut down speeds, which is of real practical value in a vacation camera.
The flash mechanism is also smoother. The flash does not open unless you press the button on the F770EXR. On the F550EXR, the flash always opens and you must explicitly hold it down or push it down to get it out of the way. When you decide you want the flash, you then have to get a finger nail underneath the edge to pry it up again. Can you say CLUNKY?
When you are done, both flashes are pushed back down. The F770 flexes a bit so you need to have some leverage to make sure you can guide it down.
The video tells the tale.
For those who are wondering, this video was shot in a room with covered windows in late afternoon at high ISO on a D7000 with Tamron 28-75 2.8D set at 2.8 (manual focus.)