Now, if Firefox auto updates in the background like Chrome, I might consider giving it another chance. When I want to go on the net, I don't want to wait for my browser to update.
The "tell you" part is the only difference between the workflow for current Firefox updates and Chrome updates, in fact... And yes, Firefox might start doing them silently precisely because of the purely psychological issue you describe.
How do you know that? I assumed Chrome did update in the background because it uses Google's Omaha project, which supports updating when the system is idle.
"attempt to update application when the user's machine is idle"
For my use cases, the two situations are actually equivalent, since my browser starts at boot and only shuts down with the OS or when I decide I should really install the security update.
For me (and apparently a large number of people in this thread), I won't consider switching to Chrome until they get more powerful extensions, namely TreeStyleTabs and Vimperator/Pentadactyl. The current stand ins completely pale in comparison.