What's faster for including scripts, using CDN (Google) or storing them locally in website's root?
If you mean the core jQuery libraries, use the google CDN for an internet-facing site (as opposed to an internal one).
The CDN has the following advantages you'll find hard to compete with:
Though you can configure the cache headers just like they do, you probably can't serve the file faster. That being said, the library/CDN is only part of the puzzle. Miscellaneous plugins and code you have should also be minified, combined and served via gzip.