First have you and Dictator even played The Order?
Because Dictator comments on tons of stuff he has never actually played.
Well I comment based upon lossless videos and screenshots. Regarding rendering, it is not necessarily something that needs to be running in front of you to comment on it in an informed manner.
Skin: Probably better in the order because I believe it has back lighting, but you really would need to do like for like tests, with a lot less PP covering up what the skin looks like in both games.
Hair: RoTr for rendering quality and simulation, I really like the shading and shadowing as well. I think the best hair in the order is galahad (sp)
Lighting / Shadowing: Both have high resolution crisp shadows and volumetrics, I prefer SSR to things that do not use it though, indirect lighting in caves looks good in RotR, but the overworld lighting in the order, in spite of being baked, is probably better. HBAO+ gives great definition to small objects though.
Overall shading: the order - metals look better, glass looks better, cloth looks better
animation: I have no idea, they both look like great animating games to me
Facial animation: Lara looks great, galahad looks great - wash
I can understand thinking they both get in punches against one another. Especially regarding character rendering quality.