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How big is the performance difference between these two processor

Solution
if your not gaming the i5-4440s performs significantly better in application overall.

The i3 has better single threaded performance, uses less power and is cheaper.
i3 4330 is dual core hyperthreading @3.5GHz, i5 4440S is quad core, no hyperthreading @2.8GHz. Honestly, the i5 is a better overall chip, although you won't personally be able to see any performance difference, the computer will. the i5 4440 (no S) would be an even better option, especially since it is cheaper than the 'S' version and the cores run @ 3.1GHz