I am doing the same thing at the moment - moving from an Ubuntu 12.04 box to a 14.04 box.
What worked form me in testing was to build the new box as per the production install guide and make sure it is working. Following that I dropped the DB, dumped the db from the old server, re-created the dbs on the new server and restored the dumps and ran the db:migrate as per the update guide.
This worked for my dev no problems. I am, however, I am now trying to move it into production and am having issues following the restore - I have a thread open today on this. See what happens.