RSS & Atom feeds are free ways to push content update notifications to people who choose to subscribe.
I'd not actually heard of Feedblitz. It looks like a service you pay for that will send out e-mail messages to subscribers.
In my book RSS/Atom would win out over a paid 3rd party e-mail service for content notifications. E-mail is notoriously problematic for this due to filtering and other blocks. Even though e-mail may be opt-in somebody's eventually going to forget they subscribed and report you as a spammer. That could never happen with RSS.
Also, with RSS/Atom you have complete control of what is sent out and when. You can change that content any time you want. Once an e-mail is sent you can't recall it. XML feeds will reside on your server for as long as you want. If an e-mail subscriber deletes your mail that info is gone.
RSS/Atom and e-mail serve different purposes. If you want a newsletter then e-mail is great. RSS/Atom is a service that you provide to allow for syndication of your content and/or notification of new content on your site.