Stephen Shore shot those using an 8x10 Deardorff camera and a 305 G-Claron lens on Kodak color negative film, then printed them on Kodak paper possibly on RA-4, however I am not sure if that process was in use then. He teaches at Bard College and will answer your question if you email him directly through his school email address.
Eggelston uses the dye transfer process for printing and achieves his colors that way. Todd Hido will answer your email, too. Try contacting him through his website. He shoots color negative film, though I don't know which brand. They are printed for him, most likely by lightjet or inkjet after scanning.