I don't think that there are any major pros or cons to either method. You're still hooking up to the samer server at dreamhost, just using different protocols. I think it all comes down to personal preference.
Generally pop3 clients can be set to store the messages in whatever folder you want, so even if the default is to dump all three addresses into the same inbox, you should be able to change this.
Imap messages are traditionally stored only on your mail server. It's kinda like having a program on your computer(s) that acts like webmail. It doesn't matter where you hook up to your E-mails: home computer, public terminal through webmail, or an office computer with Thunderbird - all ofyour E-mails will be there, and if you read the E-mail at home it will be marked as read everywhere else.
So if you got a bunch of Junk mail, had your home computer filter it out to only the real messages, then when you log onto webmail from work later that morning you'll only have the real E-mail messages, then junk won't still be there as it would with pop3.
You can accomplish a similiar thing with pop3 by haiving your E-mail client leave a copy on the server. But if you delete an E-mail or read a few, they will all still be on your server when you log into webmail.
Imap normally requires a constant connection to the internet though. I know thunderbird can be confiugred to store a copy of the messages on your computer so you can access off-line. But for the most part if you're using imap you'll want to be on-line. That one may or may not be an issue for you.
I think those are the basics anyways. I use imap because I dual boot my system and access E-mial from public terminals on a regular basis. I also have thunderbid at home keep a backup of all my E-mails encase I loose my intenret connection or dreamhost has some data loss.
Hope that's helpful.
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