I am sorry you are having trouble understanding this. I must not be explaining it well. I will try again.Maybe I'm not reading what your saying correctly or perhaps you didn't word it correctly but the buoyancy characteristics of a tank definitely matter.
I'm not talking about the buoyancy swing but the absolute buoyancy of the tank when (near) empty.
A Faber 12.2L standard cylinder (steel) has a buoyancy of -0.75kg (1.7lb) when empty.
A Catalina S80 cylinder (aluminium) has a buoyancy of 1.27kg (2.8lbs) at 500 psi and 1.86kg (4.1lbs) when empty.
This means that you can carry up to 2.5kg less (extra) weight when diving with the steel 12.2L tank versus the 11.1L aluminium tank.
Your buoyancy depends upon the weight and volume of the total package--you, your gear, and and your wetsuit, your tanks--everything. So let's say diver A and Diver B are doing the same dive, and they miraculously have exactly the same buoyancy characteristics in every way except their tanks. Diver A is using a Faber 12.2L standard cylinder (steel), and Diver B is using Catalina S80 cylinder. Since you did not give this information, I will assume that the tanks both have the same external volume. You also did not give their weights when full, so I am going to guess that the Faber weighs about 6 pounds more than the Catalina. That means that at the beginning of the dive, both divers have the same total volume, but Diver A is 6 pounds heavier than than Diver B. Diver B must therefore add 6 pounds of lead to have them both the same at the beginning of the dive.
Let's say that they now have the same volume and weigh the same, and let's make that 226 pounds. As they dive, they both use up 6 pounds of air. At the end of the dive, they will both still have the same volume, and they will each weigh 220 pounds, because they lost 6 pounds of air during the dive.
How will the difference in the composition of the tanks affect the change in the buoyancy of the total package as the divers use their air?