I think I posted in the relevant LOTR thread once upon a time, but an archival 35mm screening at MOMA of Fellowship of the Ring showed colors that were shockingly similar to the EE BD. To my eyes, the EE is a slightly misguided, quick attempt to recreate the photochemical theatrical colors on a digital basis, but the TC’s colors are far from what was seen in theaters.
Even the preview for Two Towers at the end of the print looked markedly different than the BD.