The kind of people involved with Mozilla, and the kind of structure Mozilla aspires to be, makes it logical for them to dismiss their CEO in the way they did.
The kind of people involved with Dropbox, and the kind of structure Dropbox aspires to be, makes it logical for them to defend their board of directors choice and not back down.
(FWIW I have deep disgust for some of the actions taken by both Rice and Eich.)