Well, local storage speed greatly depends on the browser the client is using, as well as the operating system. Chrome or Safari on a mac could be much faster than Firefox on a PC, especially with newer APIs. As always though, testing is your friend (I could not find any benchmarks).
I really don't see a huge difference in cookie vs local storage. Also, you should be more worried about compatibility issues: not all browsers have even begun to support the new HTML5 APIs, so cookies would be your best bet for speed and compatibility.