Although what I like about gmail is that the mail is stored on Google's servers and I can read it anywhere, I use Thunderbird more because I have 5 email accounts set up on my mail provider - one for family, one for bills, one for business, one for catalogs and other junk and one for website registrations - and Thunderbird handles them all in one window, local on my machine. Kinda. When I am traveling, I forward any email I think I will need to my gmail acct for access while not at home. Cumbersome, but it works. Alternatively, I can set up email forwarding on my ISP's server or read mail as webmail, but I really hate Centurylink's webmail client, it's extremely clunky.

I switched away from Eudora back when it went to Qualcomm and really didn;t care for Thunderbird as much, but I've gotten used to it over the last 5 years or so.