Transitioning between different mail servers is very easy when using IMAP. All that you need to do is to configure your mail client for both accounts, and then just drag the mail messages and folders between the two.
I did this to move the mail to the new server, and I noticed some interesting things in Mail.app when transferring these messages.
- When copying a folder that has both mail messages and other folder, the messages in the root folder sometimes didn't get copied
- Mail doesn't deal well with a IMAP accout that is above it's disk space quota. It just states "Unknown Error". (Thunderbird handles this well.)
One thing that I noticed that Mail.app did was, that it handles losing the connection to the server well. I rebooted my Airport while copying over 1000 messages. The copy stopped. When the connection was re-estabilshed, Mail restarted all "Pending" actions. I don't know if this is in the IMAP standard, or if Mail.app just remembers the list of commands that need to run, and keeps trying them until they have successfully completed.