Tool AIs and Agent AIs given the same task will not lead to the same outcomes, nor result in the same routes being taken. However, they are likely dangerous in broadly similar ways, and many warnings and precautions for one of these apply also to the other.
Then formulate a weaker version of the theorem that you think is true.
Tool AIs and Agent AIs given the same task will not lead to the same outcomes, nor result in the same routes being taken. However, they are likely dangerous in broadly similar ways, and many warnings and precautions for one of these apply also to the other.