Over the years I have used Mozilla products a lot and have come to trust them.

One key point to note with both Firefox and Thunderbird is that they install their binaries and products stuff in one directory and then everything "user" related in a profile.
Sometimes you need to move this profile though, from one computer to another or from one directory to another. Moving your profile folder is well described at Moving your profile folder - MozillaZine Knowledge Base which contains a link to articles specifically for moving from Windows to Linux and also Thunderbird profiles.