Maybe I missed it here, but what (in your opinion) *is* Linux's dirty little secret ? I'm assuming you liked the Ubuntu package manager, but the issue of not knowing where it installed to isn't important - if you install it with the package manager, use the package manager to remove it! To run it, go to the menu and run it, or open a archive, or run the app name from a console (to run FF, just type "firefox" and hit enter).
I agree that the many package formats can be irritating, but there are always solutions, be it converting it, finding a pre-compiled one for your distro, or getting a plugin to get the package manager to use it...