stock-clocks to stock-clocks the most of the i3s mentioned in this thread will be similar-better in gaming (it's debateable on the newer games, they're more optimized for quad-core+ usage) than the 6300/6350.
However, buying an after-market cooler with the 6300/6350 will allow you to overclock, which will destroy (literally) the i3s in gaming, encoding, playback, video editing/rendering and more.
IF you can find a quad-core i5 within your price range, WHICH HAS 4 CORES, go for it. It is highly likely that this will destroy an overclocked 6300/6350.