The answer really depends on what their goals are. If both big fiends are stranded, and just want to leave, they will behave differently than if they came to the Prime intentionally to destroy a powerful good enemy. I'll hypothesize about the second one in my example- a pit fiend and a balor trying to undo an enemy.
LE fiends like heirarchy, and structure, so long as they control it. They like power games. The Pit Fiend would, depending on your cosmology, summon little buddy devils to help it, and then move in and start working on something they could corrupt. A temple, an order of knights, a bureaucracy or king's court. He might make alliances with powerful evil beings he couldn't outright order around. The Pit Fiend would get his target patsy under his control, and then go after his real enemy, whatever it was. Corrupting the initial group is just a side bonus. He mightn't really care to destroy his target, either, more subvert it and bend it to his will, and have it turn on its friends.
CE fiends like power. It's all that matters. A balor would find himself a lair, and start gathering lackeys, bullying them into aiding him, and do everything he could to take down his target. Destroy it, grind it under his heel, and make sure everyone ever associated with it was cruelly used and ultimately destroyed. He wouldn't be dumb about it, but his methods would be more direct than the pit fiend.
In Sepulchrave's story hour, Grazzt has attempted to attack the heros directly several times. Once he waited for them to attack a half-fiend he knew of, then sent in several powerful demons to lay the smack down. Almost worked, too.
The devils, on the other hand, haven't done much that we've seen, I think, but the temptation of Mostin the Metagnostic (offering him a demi-plane to serve the archdevil) happened offscreen, and the temptation of Eadric the paladin is still pending. What will they offer him? It's going to be good
