With IMAP you can see ALL messages in your Gmail account. At least you see only the headers, only when you click on a message the body (email speak -> the actual content of the message) will be downloaded and you can read it. If you assign tags or how it is called in gmail, these tags are seen as folders when you access gmail per imap.

With Pop you download the whole message and depending on how you configured your gmail account settings (in gmail, not the Bat!) it either keeps your messages in gmail and marks them as downloaded or deletes them or ... (look it up in your account settings). If you want to download your mails again from gmail via pop you need to do some quirky things and it isn't precise (either you can download ALL mail again or recent ones (last xx days))

Soooo, I mainly use pop with gmail. For getting all mail again to another client or another The Bat! installation, imap is great. Or if you want to upload all your old mail to a gmail account it is great, too.