The 3.8 is known to eat oil and is pretty slow with the 4spd auto. The 3.6 is more efficient, more powerful, and you get a much better 5 speed automatic (if you're into autos). The 2012 MY eats cylinder heads, but the warranty on that is extended to 150k, so nothing to worry about. Otherwise, there are relatively minor and rare issues with the Pentastar that include water pump bearings, casting sand in the heater core, and cracked oil cooler housings.
The interior and tops are also much better on the 2011+ (although the 2011 has the older powertrain).