i3 is 32 nm , core 2 duo is 45nm , i3 is more economic , less heat , and is faster.
i3 and core 2 duo are both dual core.
Quad core have 4 cores , the diference between old quad core and i5 is the same like the dual cores.
If you use software what is CPU dependant you need an quad core ( i5 ). Slowly all the games, software and aplications are made to use multicore ,then a quad core is the best choice and is more future proof.
For a budget PC used for gaming an i3 is enough but you don't know for how long.