Duel: Archdevil vs Archangel

No, I don't think they depend much on the environment... I, for some reason, never take it into account. But comparing 1v1 is not necessary! Such a situation won't happen in reality! (unless, of course, you set it up yourself.) Which of them is more useful? Here, devils summon lords, and archons resurrect, and without considering the circumstances, you won't be able to figure out which is better. I don't remember their price either; I think devils are more expensive, but... If you like demons, will such minor details bother you? No! But demonesses shoot in a chain! So Legolas is right; people choose the one they like more.
As for strength... it's been said many times: you can't figure it out just by theory...