The biggest difference as far as I can tell after some testing is not which way the binaries have been built (either by you or the package maintainer) but which version you get. I tried just now on my machine (Ubuntu 14.04) with the Cahn-Hilliard demo.
It runs in 52 seconds with FEniCS built from source and in 40 seconds with the Ubuntu packages. The main difference is here that the packages are version 1.3 while the from source build is using version 1.5+. Generally, later version should be faster so a regression might have been introduced (calls for further investigation).