The manual says that reading out a single eulerAngle isn’t reliable (even if it did sometimes work.)
So they can both face any direction, but the “roll” should be as equal as possible? Could abuse LookAt to copy #1’s UP into #2. Will “flip” when obj2 is facing opposite obj1, but might still look nice:
The LookAt won’t change the way you face, but will “roll” obj2 to try to align its up with obj1’s up. Alternately, if you’re already using a lookAt, toss in the alternate up there.