Cleaner code, the seperation of content from style.
And more importantly than that, the positioning of content within the page source.
<header> <navigation> content <footer>
content <navigation> <header> <footer>
It also creates smaller size pages, generally. And almost always a higher ratio of "content text vs. markup text".
Don't forget the user perspective either (thinking like a user is the first step in truly understanding SEO) - getting tables to render on mobile devices is tricky, and that's becoming more and more important. It's not inconceivable that at some point in the future SE's will serve different SERPS to users on mobile devices based on accessibility.