A lot. The focal points used for the autofocus are much greater in the A6300 (so significantly faster focusing). The sensor and processor have pretty huge improvements in the A6300, including low light function. There are plenty of other differences that are very easy to find with a simple online search of "A6000 vs A6300".
Unless you are a pro, you probably don't care and the A6000 is good enough. If you are shooting video, the consensus seems to be the A6300 is a must over the A6000.