I think the Steel devils would act very directly in this regard. If they have a goal, they march towards it, warn obstacles to move only once, and strike down or bully anything in their way. Anything too strong to strike down or bully might be moved around, but they'd remember and make sure to report that devil as a critical obstacle to their given orders. For Orthans, however, they make sure to cut from behind and forward. When questioned later they bluntly tell a commander 'You had given us our objective, they didn't move when signaled them to, and we had no time to wait. So we made a path.' The more underhanded or manipulative units of Steel devils may even let themselves be 'unfortunately waylaid' and let Orthons engage with an enemy first until weakened. That way when they come in killing, and the Orthon falls, they can claim the enemy did it and they were avenging a superior devil. Their commanders won't believe them, but in lacking evidence and the successful completion of the mission they'll likely get away with it. If they fail some great objective due to the absence of an Orthon, however, you can expect those Steel devils to get tortured, demoted, or maybe even sent on a suicide mission if the commander is merciful.
From the Orthan's perspective, life is a hellish torment and they seek rapid escape from it through accomplishments. Steel devils, and most weaker devils, are likely something to take frustrations out on and send to die on every hill. The mad commander who orders units of the troops he hates to hold every meaningless hills and achieve every meaningless victory. To suffer and die for nothing while he hunts for glory. Glory he feels he will need to get permissions to take his next devil rank and remove the spikes of torment holding on his armor.
Its a match literally made in hell. The abusive, but obediant, glory-hound commander and equally cause-loyal, but marginalized and furious, soldiers who will kill him when given half a chance. You can probably draw some parallels to Vietnam commanders and getting 'fragged' for some inspiration: https://en.wikipedia.org/wiki/Fragging
Its probably important to remember that both groups of devils are absolutely loyal to the greater cause of devils and will put aside power-vying if ordered to or in dire enough straights. They are willing to band together with rivals against demons or celestial over losing the day, but, until its a direct order or obviously necessary, everything they do is for themselves in an effort to game the system and achieve those promotions. Office politics on the battlefield.