As far as the advantages of a newsletter over a feed, nothing comes to mind. At least not from the perspective of the average RSS user. It does help the distributor of the newsletter gauge interest in some capacity, but as @Echedenyan mentions in the cross-post, this also provides the distributor with a bit of personal information and the ability to send additional emails for advertising.

On a personal note, I find newsletters somewhat bothersome, since they quickly fill up mine inbox and only distract from the emails I need to read and respond to. In the end, these newsletters pile up unread and are eventually purged, since I don’t think to check my mail in my free time. One’s workflow with email will determine if newsletters are more convenient than a feed.