I do see a difference.

Eich's stance was (and is) personal, and I'm pretty sure it would have stayed that way. I would have kept using Firefox because of the Mozilla position on privacy and openness, and despite its CEO position.

On the other hand, Dropbox is a private company. They don't stand for you, they stand for themselves. They are their own first priority. Having someone as important as Mrs Rice on board is certainly not something that will be beneficial to the public. If she's not there for the public but for Dropbox, then yes, we must fear the worst.