The I3 is a good processor but it is still a dual core. It is basically a G860 with hyperthreading.
In everyday use (web browsing, email, word processing, etc) the I3 will be equal to the 965. Run a heavily threaded game or application and the 965 and FX CPUs will simply walk away from the I3.
If you look at benchmarks for Crysis 3 and newer games / applications, software is finally taking advantage of those extra cores. Also, keep in mind the PS4 and next XBOX will be running 8 core CPUs. Once those ports start coming out I don't believe the I3 will have the horsepower to run them.
Honestly, I would highly recommend spending the extra $45 and getting the FX6350.