There are people who state they prefer Claws Mail to Thunderbird but then admit they have not used both side by side. People who have used both side by side usually prefer Thunderbird. There appears to be very few differences. Both have basic email you can extend with add on modules. Both arrive with RSS readers built in because RSS readers are almost identical. Both require an add on for calendars because calendars require different code.
Evolution is another alternative but is not a good choice if you use Windows and want to convert your email application on Windows before converting to Linux.
Claws Mail is light and efficient with small amounts of mail but does not have anything to handle large quantities. Thunderbird was going to use the SQLite database for all high volume operations but currently uses SQLite only for settings. The first email client to use a database for indexing all email will become a clear leader for people with a huge collection of email. Users occasionally comment that Claws Mail is hopeless handling more than a few accounts while Thunderbird is fine with many accounts, a characteristic you would expect with Thunderbird using a proper database for account settings.
Thunderbird works reliably on every useful operating system. Claws Mail has downloads for a lot of operating systems but does not have the same wide range of support on Windows. If you are a Windows user looking to migrate to Linux and want to convert on Windows, support for Thunderbird is better than for Claws Mail. After you eventually convert to Linux, there is no real reason to convert from Thunderbird to Claws Mail.
Individual users might find Claws Mail fine. Web site administrators with dozens or hundreds of email accounts will find Thunderbird the better choice. For anyone else, you will have to look through the add on modules to find the modules you want then use the email client compatible with those add on modules.