Possible? if(aGameObject.transform != bGameObject.transform)

Can you compare transforms like that to check if an object moved, scaled or rotated?

Or do I have to specifically check?
aGameObject.transform.position != bGameObject.transform.position

You need to check for specific changes. If you use transform == transform it will check to see if the transforms are the same transform component, not the individual properties of them.

Also keep in mind that if you say Transform a = someGameObject.transform and then somewhere else say someGameObject.transform.position = Vector3.zero then a.position will also equal the new Vector3.zero since the variable a points to the same Transform component as someGameObject.transform