Added to the suggestions above.. I would also conduct a simpler test and start eliminating variables.
Batteries are swappable and inexpensive for the most part so simply discard the older generic dubious set and use the same fresh set for both cameras.
I would then start by taking both cameras and taking a meter reading with NO lens attached. Same batteries, same NO lens. My FM2n will give a reading.. I believe the FE will as well.
Check the deviation on that and then add the lens variable with the same battery set.
I once did a similar test to check the meter on a couple of camera bodies I had and see how much they deviated from each other. I found it easier to do this at night on a white , (somewhat) evenly illuminated wall.