The differences between the original version of Pandemic and the 2013 version are essentially cosmetic. The only significant change is to the Role cards. The 2013 games features 2 new roles, Contingency Planner and Quarantine Specialist, that aren't in the original version. It also has the revised Operations Expert from the original On The Brink expansion. There are pictures of these cards here. There have been some changes to the rulebook to clarify some things in the original rulebook that caused confusion.
The original Pandemic is not compatible with the 2013 expansion packs (the card backs have different designs), however you can buy replacement cards to make the original Pandemic compatible with the new expansions.