As far as I know they both had support from their respective boards. But Rice was 'only' up for the position as board member. Eich was to be the highest public and private facing position of the company. The controversy surrounding him, unfairly or not, also affected people personally. Basically Rice only needed the trust of the rest of the board, while Eich would have had to fight to run or represent the company. Your own comment being an example of how the Internet doesn't easily forget things.
Contemporary events for another notion you wouldn't find "outside California and college campuses" succeed in toppling Brendan Eich at Mozilla. The only difference I could tell then was that the Dropbox board put its foot down in support of Ms Rice and Mozilla's board folded.