My initial comparison between PSF measurements did not look very good. I compared the ellipticities and sizes of the stars and psf model between matching objects in HSC vs. LSST. Here is a difference in e1 for the stars used in measuring the psf on visit 1322:
This shows a large difference between the two, which was puzzling because I verified that the images themselves were nearly identical. Also, the rms of the residuals from both LSST and HSC were the same size. So each thought it was accurately reconstructing a good model of the psf. The discrepancy was not as bad for other visits like 1226:
I believe the difference here is due to using a different initial psf model that is used to measure the centroids of stars that are input into psfex. In HSC, the initial psf is a Gaussian of fwhm=5.88 pixels. In the new LSST framework, the default settings do two iterations of finding the psf model, where the second iteration uses the estimate from the first. If the actual seeing is smaller than 5.88 then on the second iteration the centroids can shift. Here is the difference between the sdss x and y centroids for visit 1322, where fwhm=3.1.
If you fix the number of iterations to 1, so the same size psf is used, then the ellipticity differences are much smaller (note the change in scale):
This can also explain why some visits did not look too bad. If the psf width was close to the initial HSC width then the discrepancy was smaller which was the case for visit 1226.