An examination of the HD broadcasts of the DVD version has shown less anti-noise processing. That plus the way they were captured makes them as good if not better than the later blu-ray release. Especially the way they have been presented for us thanks to Schorman. He also preserved the PT and that is the best quality for the DVD version of TPM and probably the best version of AOTC and ROTS.
The theatrical 97 SE has now been preserved in a scan from 35 mm. I don’t think it has been cleaned up fully and it has not had the color restored. Outside of that there are SD broadcasts from Europe that preserve those version at higher than LD quality. I would call them near DVD quality, but they suffer from missing frames and being PAL. That is also the best preservation of the full original TPM theatrical version.
Currently the only versions not preserved in any form in HD are the 97 SE of TESB, ROTJ, and the theatrical version of TPM. The original TESB and 97 SE ANH are currently unfinished and only in grindhouse form.