Mozilla business model is entirely built around their market share. As such, they are in a much more difficult situation than Google's Chrome team. If Mozilla has a difficult time (financially), they are more likely to do shady things than the Chrome team which has no such pressure. For example, the Chrome team would never accept any cryptocurrency deal; something that I have no difficulties imaging Mozilla to do.
Obviously, Chrome will not actively hurt Google's other businesses (specifically ads), but Chrome's primary goal is to make the web a better place. The worst case scenario for Google is that the web (and thus their revenue stream) disappears.