1 -- Don't take this the wrong way, but without learning about photography, neither camera will give you "great images." They may give you slightly better images than you were getting with your cell phone. The auto on a great camera will produce better pictures than auto on a cheap camera because the camera has some greater capability. But in the end, you will only see some improvement.
2-- As mentioned, do you see yourself buying additional lenses? And WHAT types of pictures do you want to take? Do you want to take safari pictures, for example? If so, you can't really do it with the RX100, and you would NEED additional lenses with the A6000 to do it.
3-- How much of a concern is size? The A6000 is fairly small,but the RX100 is much smaller.
4-- How much of a concern is a viewfinder? The RX100 does have one, but it is small and a bit hard to use, IMO. The A6000 has a nicer viewfinder.
5-- How much real action do you wish to photograph? The RX100 will do fine with kids walking around, but if you want to do sports, for example, the A6000 autofocus is much faster.
6-- Pure image quality --- Will be close. The A6000 has the greater potential for better image quality, if you add hundreds (or even thousands) of dollars in additional lenses. But out of the box, the lens you are considering for the A6000 is a very good lens, but F4. The RX100 lens is "faster" at 1.8-2.8. That means, you can use the RX100 at a lower ISO than you would use the A6000. If you added a 1.8/2.8 lens to the A6000, the A6000 would give you better image quality. But sticking with the F4 lens... the image quality will kinda even out. It will be very close.
