Which gas will make a beer last longer in a keg, CO2 or nitrogen? Is there a difference in how long a beer is considered good when running through a nitrogen system vs a co2 system?
I don't see CO2 versus nitrogen making a difference in freshness. You are probably thinking that because nitrogen is an inert (ie non-reactive) gas that is used in some packaging to extend the shelf life of some foods like fresh pasta, using it instead of CO2 would extend the life of your beer. However, beer already has significant amounts of CO2 dissolved in it so using nitrogen isn't going to keep it any fresher as a result. 

Nitrogen is used versus CO2 because some people like the texture it creates as opposed to CO2, however that's a separate topic which has already been covered in another question.