I do both, but use them differently.
The blog is for short posts, news and updates, and there's no guarantee on when I'll post. The newsletter is monthly and it's always a new essay or new writing of some kind.
As much as it seems everyone has moved to blogs and RSS/newsreaders, there are many folks who prefer to read e-mail, or who like to have something to read when offline and commuting to/from work.
If you're looking for a blog site, or blog software, I highly recommend wordpress. You can host a blog for free at wordpress.com, or install wordpress on your site. I've been using it for years, know the founder of the company and recommend it.

