From what I've read, because of the 6 speed transmission the 0-60 is a bit quicker and the gas consumption is slightly better. The 2013 model also has a new navigation system software, and blind spot indicators. The new Hondalink software is capable of streaming online music(i.e. Pandora) with the CT's stereo when you tether to a cellphone for internet connectivity.
The biggest gripes owners/reviewers had for the 2010-2012 models were, the navigation system software was dated and a lack of blind spot indicators.
The changes I mentioned on the 2013 model are the ones that stuck out the most for me.