I am thinking about getting the A6300 with the e-mount 16-50, but would love to use my A mount 16-50 as it is simply a killer APS-C lens for times when I really need either the speed or the lens quality.
I would love to add something intelligent to this conversation, but I don't have either the LA-EA-3 or the A-Mount 16-50/F2.8 lens.
But, I have the a6300, the PZ 16-50, an LA-EA-2 adapter, a few E-Mount primes, and a few random A-Mount zoom lenses.
Here's what I currently think I know: The adapter will change your brand new a6300 into the latest, greatest version of your old camera. That's not all bad, especially considering how much you paid for the older Sony lens, and there isn't a direct E-Mount replacement.
But it's not all good either.
If you're shooting with an older A-Mount camera and are happy with it, I'd stick with it. Otherwise, you'll have to consider buying the Sony/CZ E-Mount 16-70, F/4 lens and giving up that last bit of faster exposure. Overall, the Image Quality is about the same. Sensors have gotten better and acceptable ISO is in the stratosphere compared to just a few years ago.