Well basically it all goes down to the archtecture.
i3 processor is based on 32nm fabrication while core2duo is based on 45nm or 65nm fabrication
(32 is new and better)
i3 processors use the new LGA 1156 socket while core2duo's use old and outdated and dead socket LGA 775
i3 has 8mb cache will core2duo's have 6mb(correct me if i'm wrong in this numbers)
while both have 2 cores