Boulderjohn nailed the buoyancy.
On trim shift, there should also be no difference. If all the parts of the diver stay firmly attached to each other.
Say we have:
- a diver (plus some diver lead)
- a steel tank
- an AL tank plus some tank lead.
So that the steel buoyancy equals the aluminum plus tank lead buoyancy. Say both tanks have the same shape, and let's ignore the lead volume.
Trim out the steel tank and diver using the diver lead. Now clone them and swap tanks.
Restoring the trim with the aluminum tank's lead should put the lead in the spot that makes the two tank packages have identical mass centers. Otherwise, you would not have restored the trim. If you want them trimmed out in 3D, the tank lead needs to go on the tank sides. If you just care about head/toe and left/right trim, the lead can go on the BC or diver. And by trim, I mean a balanced weight distribution such that the diver with all their gear has mass and volume centers are in the same spot.
Now we breathe down the gas. Mass leaves each diver from the center of the two tanks. Which have the same shape, so the trim shift is the same. Both tanks will be getting lighter. The steel tank will press less strongly downward on the body. As will the aluminum tank, in equal amounts. From the same spots.
If the aluminum lead was attached to the aluminum tank, there should be no differences.
If the aluminum lead was attached to the diver's front weight belt, and the tank is only attached to the diver at the shoulders, then the aluminum bottom will eventually start floating up above the diver, changing the shape and mass distribution differences between the two divers. But that would not be the case if the tank was firmly attached to the diver, or at least to the tank's lead, at top and bottom.
That is how I read the physics of the trim.
Steel and aluminum tank walls have different thicknesses, and the tanks often have different pressures. This means equal displacement and equal gas volume tanks are unlikely. Steel lets us build different tanks, so we do that. But the trim shift is due to the amount of gas, its location, and attachment to the diver, not the metal that holds it.
I know empty aluminum tanks float up if not tied down, I'm a side-mount diver. Our tanks are attached with line, bolt snaps and bungee cord, not 2" webbing.