Upon opening Thunderbird for the first time you are asked to import an e-mail inbox. It is similar to filling out the account information in Mail. You'll need the e-mail address and the incoming and outgoing servers for the account to be set up properly. Once set up, it should import all of the mail from the server.
Thunderbird has every option that Mail has. You can Get Mail, Write Mail, Reply, Forward, Save messages, set up a Junk Mail folder and so on. About the only thing Thunderbird does that Mail doesn't do is have Add-ons, but those are only for reporting system crashes so it's not that big of a deal as your Mac will also report crashes to Apple if you so wish.
Thunderbird's interface is easy to use and understand, if you are familiar with Mail. The biggest problem, however, is that you can't import a GMail account. Thunderbird doesn't allow you to choose a SSL port for incoming or outgoing server, which is required to import mail from GMail. This is a big downside, in my book, as my primary e-mail address is a Gmail account
Thunderbird does have a lot of safety precautions like protection from phishing, but none of that really matters if I can't use the software to get my mail.