About 18 months ago, I moved from Eudora to Thunderbird. To accomplish the move effectively, I needed to use Aid4Mail. I started by downloading a limited trial that would move just a few messages, and it worked, so I paid for a subscription and migrated my entire email history plus my contacts. According to the web site, it can move archives from LiveMail to Thunderbird, so I think it would be worth your investigating.

I'm generally happy using Thunderbird. The main problem I've had is controlling the format of email I'm composing. I'm often unsure whether what I'm seeing looks correct on my screen because Thunderbird has inserted formatting to force it to appear that way or because Thunderbird has inserted no formatting and it's just using my display defaults. Sometimes what I've written comes back to me quoted without modification, and the quoted version looks horrible, so I need to assume it looked equally bad when my correspondent received it.

I've also had some problems where the display refuses to switch to a new message when I click on it in my inbox, so I need to make a more radical switch (such as opening a different folder and coming back to the inbox) to restore responsiveness.

It's definitely an improvement over the last version of Eudora, but it's not as good as I'd like.