Natural pb will either be just peanuts or peanuts and salt. Organic means that the peanuts are organically grown without pesticides and such. Most organic pb is natural but I guess its possible for it not to be and natural doesnt imply organic.
As far as pro/con, it just depends if you prefer organic food. I personally havent found an organic pb that I like better than my normal one so I just stick with the regualar natural.
Organic peanut butter tastes like crap, unless your worried about pestacides and such that were used to kill bugs on the plants go with normal peanut butter...