You've written your own reply. You wrote that the vBulletin PHP mailer takes 3 minutes but overloads the server, and that SMTP mailing takes 15 minutes.
You don't say, and I don't know, what method your PHP mail function is using. But it appears to be creating multiple processes to deliver multiple emails. That's creating the problem you're experiencing. The exim SMTP input is self-limited, based on settings in the exim.conf file and/or the exim startup command line.
You really can't compare your new server with another server because of the variables involved, such as system speed (processor speed, disk speed), mail server (exim, postfix, sendmail, qmail, etc.), connection speed, and the amount of preprocessing done by your mailer (exim runs all SMTP email through SpamAssassin, for example).
Sure you can tweak the exim.conf file so exim will start more processes to do everything faster, but doing so will impact your server even more.
Do you really have a problem with taking 15 minutes to send 2,000 emails? That's 192,000 emails per day.
Jeff