Wright placed the Schmidt corrector at the focal plane, and had the mirror aspherised to cancel coma resulting from the altered aperture stop position (the aperture stop effectively coinciding with the corrector).
While astigmatism remains present in the Wright camera, it combines with the mirror's Petzval field curvature to result in a flat best image surface.
In effect, the only monochromatic fourth order (wavefront) aberration of the Wright camera is relatively strong astigmatism.
However, while the off-axis error in the flat-field Schmidt results from defocus, in the Wright camera it is caused by astigmatism.
On the other hand, the best (curved) image surface of the Schmidt is practically free from off-axis aberrations, hence clearly superior in quality to a best (flat) field in the Wright camera.