The technical difference is that the 6500 has an image stabiliser, the 6300 does not. But whether that is worth twice the price, I doubt. In my opinion, the 6300 is perfectly adequate. You can hold your hand still.

My opinion again: no not close, totally OK for photography because the 6300 (as well as the 6500 of course) has a very fast autofocus and that was very important to me. I have now taken several hundred photos in various situations with the 6300 (in programme automatic mode) and am very happy with the results. The software is very good, and the 6500 has the same software as far as I know. I think if you want to shoot a lot of movies, the image stabiliser is worth its weight in gold. The touch screen is also a bonus, of course, but from my point of view it's a nice addition. But the two additional functions cost real money, namely the 6300 times 2. So it depends - as always - on the area of application whether you want to invest twice as much.