The newly completed (Nov 2013) 840 is only 16 miles further than staying on I-40 thru downtown Nashville. Much of it is 70mph, and substantially less traffic, so it's six of one, half dozen of the other. If rush hour, definitely take 840, or if you're aware of any accidents, etc. Also very scenic, and intersects with Natchez Trace Parkway that goes to Jackson, Ms (thru Tupelo, if you're an Elvis fan), or if you are considering a more southern route west, ie I-20 or I-10.
Above may/may not be useful depending on your ultimate destination, where you planning Memphis or a different route west of Nashville?