The Edinburgh degree is a year longer because Scottish degrees last a year longer than English and Welsh ones.
I'd say to visit them both before you decide. Edinburgh was my insurance and it was a nice department. Suffers in league tables because of low student satisfaction, though; might be of some concern to you. The course looked set up nicely, too. I know nothing of Warwick as I hadn't heard of it before I started reading TSR, but isn't the course there a general engineering course? If you know you want to study mechanical engineering then the Edinburgh course would be better as it'd allow you to specialise sooner.