Somehow Firefox managed to take a huge share of the market in a very quick amount of time.
first, there was netscape, a greedy company who tried to lock up parts of the WWW with their proprietary server software and sell the browser for money. then, microsoft stepped in and crushed them with their $0 software, which was in retrospect one of their best moves - although they tried to commercialize the web with their MSN too, and it played out differently from what they have intended. later on, the netscape company was about to fail and a group started a hugh push to open source the product, that's the mozilla foundation with the mozilla browser. that went fine for some time, but mozilla was too bloated. firefox was an attempt to re-start from ground zero in order to build a browser that is just a browser and nothing more. during that time, they used google as their integrated standard search engine, which brought them a shitload of money every year. therefore, firefox didn't grew out of nothing.
i also don't see many similarities to bitcoin: bitcoin is not the versoin 3.0 of some prior systems. if bitcoin would have been the reduced open source version of a paypal client that went bankrupt, then ok, but not in that way. additionally, there was no NPO in the first place, steering the development. it happened rather disorganized and in the very first beginning, it even stalled for some time and only got more track later on. finally, there is no huge company investing a fixed amount of money into bitcoin's development every year.