I don't know the default OS X client so I can't go into detail, but I'd guess that one is better integrated with OS X. On the other hand, Thunderbird works cross-platform and allows you to choose any operating system without having to consider a new mail client, set it up and learn new ways. You could probably even copy over your data folder and resume working without any set-up (`scp -r ~/.thunderbird user@newpc:` would be the complete migration process, assuming it works between OSes).
You're correct. You copy the profile folder and set the default profile startup to be the one you copied (I think this was in the profile.ini file) and it is if you never left. I this this between mac, linux, and windows machines and it functioned perfectly every time including add-ons, settings, filters, and themes.
I switched. Better search, better tagging, customizable layout, better peformance (apple mail often had problems with syncing flags and folders for me)