I don't think it's changed e-mail as much as it is changing mobile messaging (SMS). With notifications on mobile FB apps, you can easily bypass SMS to communicate with other friends either at their computer or on their phone.
There are still other e-mail features FB private messages don't offer: forwarding message threads, attachments, email subscriptions, etc.)
Those can all be fixed easily enough. When (not if) facebook finally launches a full-featured email service, it will probably dominate gmail/yahoo/microsoft. You would get a address @fbmail.com or whatever so you could still use it as your "normal" free email client. But you then also get easy communication with all your friends, since facebook already knows how to contact them and can do so bypassing traditional email alltogether (since the messages stay entirely within facebook's data centers). Not to mention tying in to their existing products-If you got an event invitation (sent to your fbmail since you no longer check your gmail) it could show you all the details (no reason it couldn't do that right now) and which of your friends are going etc right in the email.
There are still other e-mail features FB private messages don't offer: forwarding message threads, attachments, email subscriptions, etc.)