If you read the various lens review websites you will have noticed that some include metrics for sharpness, which are usually scores of "Line widths per Picture Height" (LW/PH) calculated with imatest. I decided to try to aggregate all of this data. Yep, I am a numbers junky and this will be very nerdy stuff so don't say I did not warn you. Also, if you don't like MTF data etc then there is nothing here of interest for you.
The websites with several reviews with sharpness measurements are:
Photozone.de
ephotozine
erphotoreview
dpreview (using dxomark data)
lensrentals
I am not including dxomark's own website data here because they do not provide the source data for the scores.
The problem is that the websites are not consistent with the camera used. A lens tested on an NEX-3 will give much worse sharpness scores than the same lens tested on an a6000. Most of the websites are consistent with the camera used for their own tests, the exception being ephotozine.
You can see the ratings for maximum centre sharpness score from each review site in the table below. I have only included the ratings for a single camera from each site. The blank coloured areas for ephotozine ratings show where the lens was tested but with a different camera from usual. [continued below the table]

[For the zooms, the focal lengths were: 200mm for the 55-210; 10mm for the 10-18; 24mm (ish) for the 16-50; 30mm for the 18-55 and 70mm for the 18-200]
You will see that the ratings are not directly comparable, in the sense that the numbers are benchmarked differently. I have run the data through a regression to calculate the relative scalings for each reviewer and taking the average of the scaled results, which are shown in the table below (worst to best), with the scores put onto the photozone.de basis. The 'obs' column just shows the number of data points ('observations'). There are five separate measurements for the Sony 50mm prime, for example.

Mostly, this lines up with what seems to be a consensus view, at least from my reading, with a few very weird results.
The big surprise is the high ranking of the a6000 kit lens (16-50mm), where the maximum sharpness (typically at f/5.6) was measured as better than the 50mm prime in both cases (photozone and erphotoreview). Owning both lenses, I find that difficult to believe but maybe I need to test mine properly. Keep in mind that the measurements from erphotoreview were done with a NEX-3, where aliasing may be a problem, although I don't know why that would affect some lenses and not others.
The two Sony main primes (35 and 50) are very low on the list, but there are five different measurements for the 50mm here and all five are a bit middle-of-the-road so perhaps there is something in that. The ratings from Lens Rentals were (I think) done with multiple copies of each lens, and the 50mm has the worst sharpness of the primes, even lower than the 16mm. The 18-55 kit lens is measured as sharper than the 50mm in two of the three measurements (and its close in the third).
Looking now at maximum edge sharpness, the rankings are:

Here the core Sony primes move well up the list while the Zeiss lenses drop a few places. The Sigma 19mm is disappointingly low ranked in both. As Roger at Lens Rentals says, "The Sony 50mm f/1.8 appears to be tuned like the Nikon 50mm f/1.4 G: it’s not quite as sharp in the center, but keeps good resolution across the entire front of the lens." I guess it comes down to your preference.
Of course, none of this takes into account lens speed, colours, distortion, 'pop', CA and all kinds of other stuff which are also important for lenses.
Cheers,
John.
The websites with several reviews with sharpness measurements are:
Photozone.de
ephotozine
erphotoreview
dpreview (using dxomark data)
lensrentals
I am not including dxomark's own website data here because they do not provide the source data for the scores.
The problem is that the websites are not consistent with the camera used. A lens tested on an NEX-3 will give much worse sharpness scores than the same lens tested on an a6000. Most of the websites are consistent with the camera used for their own tests, the exception being ephotozine.
You can see the ratings for maximum centre sharpness score from each review site in the table below. I have only included the ratings for a single camera from each site. The blank coloured areas for ephotozine ratings show where the lens was tested but with a different camera from usual. [continued below the table]

[For the zooms, the focal lengths were: 200mm for the 55-210; 10mm for the 10-18; 24mm (ish) for the 16-50; 30mm for the 18-55 and 70mm for the 18-200]
You will see that the ratings are not directly comparable, in the sense that the numbers are benchmarked differently. I have run the data through a regression to calculate the relative scalings for each reviewer and taking the average of the scaled results, which are shown in the table below (worst to best), with the scores put onto the photozone.de basis. The 'obs' column just shows the number of data points ('observations'). There are five separate measurements for the Sony 50mm prime, for example.

Mostly, this lines up with what seems to be a consensus view, at least from my reading, with a few very weird results.
The big surprise is the high ranking of the a6000 kit lens (16-50mm), where the maximum sharpness (typically at f/5.6) was measured as better than the 50mm prime in both cases (photozone and erphotoreview). Owning both lenses, I find that difficult to believe but maybe I need to test mine properly. Keep in mind that the measurements from erphotoreview were done with a NEX-3, where aliasing may be a problem, although I don't know why that would affect some lenses and not others.
The two Sony main primes (35 and 50) are very low on the list, but there are five different measurements for the 50mm here and all five are a bit middle-of-the-road so perhaps there is something in that. The ratings from Lens Rentals were (I think) done with multiple copies of each lens, and the 50mm has the worst sharpness of the primes, even lower than the 16mm. The 18-55 kit lens is measured as sharper than the 50mm in two of the three measurements (and its close in the third).
Looking now at maximum edge sharpness, the rankings are:

Here the core Sony primes move well up the list while the Zeiss lenses drop a few places. The Sigma 19mm is disappointingly low ranked in both. As Roger at Lens Rentals says, "The Sony 50mm f/1.8 appears to be tuned like the Nikon 50mm f/1.4 G: it’s not quite as sharp in the center, but keeps good resolution across the entire front of the lens." I guess it comes down to your preference.
Of course, none of this takes into account lens speed, colours, distortion, 'pop', CA and all kinds of other stuff which are also important for lenses.
Cheers,
John.
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