When I ordered the A6300 camera, I ordered the LA-EA3 adapter at the same time, because I had read that autofocus would work really fast with adapter.
With my A6000 I had used the LA-EA4 adapter with the 70-400G A-mount lens, and it worked really well. And now I looked forward to using all the focus points of the A6300, and not having a SLT mirror to take 1/3 of the light.
As I started testing the setup with A6300, I found that the autofocus worked with the LA-EA3, but not nearly as fast as with the LA-EA4.
The first video is of focusing with LA-EA3. Average number of frames from I press the shutter, till it confirms focus when going from near to far is 51 frames. And from far to near it's 39 frames. Shot with 25 frames per second
With the LA-EA4 the numbers are 14 frames from near to far, and 25 frames from far to near.
I also tried taking photos of birds on a bird feeder, but simply haven't had a tack sharp photo using the LA-EA3 yet. Guess it's too slow.
For now I will contunue using the LA-EA4 with my 70-400G, but hopefully there will be a software update that makes it work better with the LA-EA3.
On the positive side, my Sigma 50mm F1.4 EX DG HSM works really well with the LA-EA3. It always had issues with Front Focus when used on A700, A77 or A6000 vith LA-EA4. But on A6300 via LA-EA3 it just hits focus :-)