At f/8.0, the 16mm is fairly sharp.
If you use it as a low-light lens (closer to f/2.8), the corners and edges go soft, whereas the center remains reasonable.
For some composures this matters, for other composures it doesn't.
To beat the 16mm with a non-native lens means spending at least 3 to 4 times as much, anything less expensive is comparable, at best, or worse.
QC on the 16mm seems to have a worse than deserved reputation. If you see edge softness, flip the camera upside down and take the same shot. If the softness moves to the
opposite side, the lens is misaligned. If the softness remains at the same side, it is a composure/DOF issue.
A lot of complaints on the 16mm were by non-users repeating 'claims'. Also, the 16mm was initially compared to the MFT which was incorrect. The 16mm is 24mmFF equiv whereas the MFT 16mm is 32mmFF equiv. (ie. compare with kit lens at 21mm).
Also, the default JPEG settings for the NEX are fairly mild for contrast, color and sharpness. Other cameras, or workflows, have more aggressive values. Try to increase such values for more popping results (screen versus print variations).
Lastly, the NEX tends to over-expose outdoors with the 16mm. Change the EV to -1EV or less or change the metering mode and use AE Lock.
These shots show what it's good at: relatively close central subject and nothing of detail interest in the corners. One reason there are so many different opinions on many lenses is that different users use them in different ways. If you shoot relatively flat, distant scenes like static landscapes then you are more likely to find ugly things in the lower corners (or upper corners if shooting through foliage.)
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Erik
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Cheers,
Henry