I'm not so sure. It depends on how it goes on in the back end.
When permanently banning, you want to keep data on the member so you can reference it later if they try to come back. When a user willingly wishes to leave, in accordance with the site's privacy policy the standard procedure may be to actually delete all personal information and thus any way of reapplying the user's information to that deleted account.
I can't speak for Smashboards because I have no experience with Xenforo, but on AllisBrawl I actually had the power to permanently wipe a user from existence if they requested it. I did two or three times if I remember. Once that was gone, it was gone.