What you said is correct, the E ( young's modulus ) is similar, the material grades that you list are not what most extrusions are made from, 6063 is the most common, material used, and is like butter in it's T1 state when extruded
Get on the same page, we are only talking about what deflection to expect, 6063 will show a greater defection than 6061 of the same profile of the same temper and same loading, there is not a lot of difference, but enough for one grade to stand out better than the other, we have tested them physically as well as FEA and almost always have a very similar outcome, the outcome is not the same for the different grades even though the modulus does not change the rate of deflection does change
This is very basic engineering, and the link to the extrusions software is all most here need to find out what to expect for deflection with what ever extrusion they select
https://www.8020.net/tools-software