I decided to try the Google AJAX Libraries API because I personally like Google services. :)
I decided to keep using this library because I don't need to worry about the hosting of my .js files. It's also possible to call a compressed or uncompressed version of jQuery and jQuery UI. It's also possible to call older version of a library.
I didn't have bad/slow speed issue using the Google AJAX Libraries API.
I'm using this technique for my web development. If I have an application working on an Intranet, I will host the .js file on my web server.