I’ve never found it to be any more integrated with the OS than any other browser. I teach IT subjects in the classroom and online at a small conservative university and use all of the browsers for one thing or another. I’ve found or am aware of no browser that does not have flaws, significant or otherwise and my colleagues who deal directly with operating systems and browsers also use all of the major browsers at one time or another. I primarily use IE and Firefox and have had no security problems with either. Keep up on the patches and updates and most problems are precluded.
I confess I use IE at work because it allows me to access my shared drives through the Sharepoint site. Firefox is not as integrated with the tools and is a real nuisance for that. I use Firefox for all my other web related activities at work though.