one of the easiest ways to transfer profiles and faves for both firefox and thunderbird is to use one of the add ons that keeps them for you.
I use xmarks with firefox which can maintain both faves and profiles.

here is the faq for thunderbird which should answer most of your questions
Mozilla Thunderbird FAQ

Move an existing profile or restore a backed up profile

How To Manage Profiles

adding an addon to help
How to Back up Mozilla Firefox and Thunderbird

tutorial for using mozbackup
Backup Your Thunderbird Profile & Emails Using MozBackup

Thanks, I really depend on the excellent help I get here, it is appreciated.

That said, I hope someone else using AT&T for an ISP and is happy pitches in. I am keeping for now to retain my email address, one I've used for at least 15+ years. Unfortunately, it appears AT&T is working on getting out of the ISP business (what, just wireless now?). They shut down the brand Worldnet, yet my 2.0 versions of Thunderbird address the "postoffice" and "mailhost" with "worldnet" as part of the address. But, it isn't working on my Thunderbird 3.0 version. I will try to figure something out tonight. My quick look last night at the AT&T help on the web said "pop and smtp with att.jahoo.com" was the magic. But that may be only if you use their DSL... not sure, seems strange. I have DSL form my local phone company, and it offers all the services Worldnet used to offer, I just am reluctant to change may address and lose contact with many I don't communicate with often... but AT&T is pushing me that way.

I have all my personal email on Thunderbird, I use Outlook for business email. I suppose I can move the business email on to Thunderbird too (not as versatile as Outlook) but have not checked on how that is done. It appears one can't have two instances of Thunderbird on one computer. Maybe one can have one Thunderbird with multiple "accounts". I know Outlook provides for multiple accounts in one instance of Outlook, but I don't recall ever seeing anything like that in Thunderbird. Outlook is clearly the "industrial strength" email client... maybe Outlook Express has some of the same capabilities... I have never used it.

You can have as many accounts as you want in Thunderbird. I have SBCglobal, gmail and hotmail accounts in Thunderbird. I can see each account separately or go to my inbox and see mail from all three accounts.

you can have multiple accounts that thunderbird fetches the mail from and you can also set up multiple profiles in thunderbird to use them as different individual setups.

You would need to speak to someone at your Internet service provider to ask about the phasing out of the worldnet address, and find out what they suggest. Many times they offer a transition package where they actually notify your contacts for you with the new info

Thanks, from past practices I'd like to have my two active email accounts appear in functionally two separate email clients, that is each with its own in-box and set of folders. I do not object to have to pick a "switch" when I turn the email client on, e.g., Click Thunderbird and "pick/click" which email account I want to work on...then to be able to close that account and open the other, or others.

My work email account activity has gone way down in the past couple of years, guess that means retirement. Thus I don't really need all the bells and whistles of Outlook and it would seem reasonable to run everything on the same application, Thunderbird.

I have download the file "MozBackup-14.10-EN.zip" but have not yet installed it. I got it from "sourceforge.net" of which I know nothing, but as I got there from the link you provided, ravencajun, I assume it is a clean source... I haven't somehow gone astray.

I have a Maxtor backup package on a USB mass storage device and it backs up many things including Thunderbird profiles. It appears if I use MozBackup it will run and store backup data for all user stuff: mail folders, address book... and tell me how to use it to update an application of Thunderbird on another computer...I'd guess that means going to the other computer and with a copy of the MozBackup and running it on that computer, resulting in any Thunderbird on that computer being cloned to look like the TB on the source computer.

yep you pretty much have the concept of what it does.
yes the download site was the correct one. It is a zip file so you will have to extract it to run it.

Sorry, need more help... maybe I can't do a MozBackup over the home network.

I created a folder in one of my network shared areas of the originating computer/Thunderbird(2.0.0-) and unzipped the MozBackup. This gave me a file to run which I did asking it to backup Thunderbird. Everything seems to have gone well and the program was about 1 GB in size when it was done. about right to hold the Thunderbird profile. Or is there a problem trying to restore a Thunderbird 3. from a Thunderbird 2.?

I then went to my new W7/Thunderbird (3.0.-) and connected through WiFi and my home router to the sending computer. I went to MozBack up and selected restore Thunderbird. The program returned: "The backup file was not found or corrupted". Did I completely miss how to use MozBackup or is it not possible to do a restore (my objective) over a network? Maybe MozBackup stored the Profile in some other location not accessible to the W7 machine over the network.

do you know where you put the file you created? if so why not just put in a flash drive and copy the file to the flash drive and then move the file off the flash drive onto the new pc.

You could put the older version of Thunderbird on the new pc if you prefer then once all is set up then you could update it to 3. I know a lot of people have trouble with 3 and go back.
Go back to an old version of Thunderbird

that link has a link in it to older versions.
If you were not happy with 3 on the new pc you could just totally remove it and do a fresh install of 2.0

Thanks, your idea is just what I originally planned to do, and have done in the past between XP machines.

But, in W7 I am having trouble finding the folders... see my post on W7 ... finding folders. As noted in that post it may be I have to change Explorer to show "hidden" folders, e.g. Application Data. I think MS likes to hid this stuff from the general user to protect them from themselves.