Which metal would flex more?

[hanermo2]

The better A. is that it depends.

By mass the alu is 3x less rigid - and importantly it likes to ring and vibrate.
But when you get the same mass in alu, it is thicker, and thickness scales pwr 3 or pwr 4 by section size.

Steel is == 3x better than alu, in rigidity for the same mass and == 3x cheaper by mass.
Cast iron is cheaper than steel and nearly as rigid.
But cast iron is 3x better than steel in vibration dampening, 10x better than alu.

There are effectively zero commercial machines using alu in any modern machine tool bodies, if they cut something via contact (vs laser/plasma etc.).

All modern machine tool bodies are thin-skinned stressed-skin structures. All.
This means the frames are as big as possible, and very thin, and used ribs/preload/mass/anchors.
Typical thickness is around 10 mm on cast iron machine bodies, in the centres, give or take.

An extreme example are modern optical tables.
They are very very light, for what they do.
They are very very rigid, for their work volume or free span length.

Typically, an optical table might be 40 cm thick for a 1 m table, and == 20x more rigid than the best japanese mazak/integrex mill-turn of similar size, or 200-400k$ cost for the mill turn.
My numbers from tlar.

The optical table is two thin skins, and tubes inside.
When I researched them they seemed to be mostly vertical-only tubes, sometimes with various goops/ballast/members/unicorn snot/magic.
The guaranteed rigidity of optical tables is totally unbelievable.

My point.
No-one uses alu.

Here is a data point - I use Thorlabs stuff for some things.
They are a top-shelf supplier of excellent rep.

https://www.thorlabs.com/newgrouppag...tgroup_id=9222

NOTE: !!!
1.7 um / 150 kg load deflection (constraints).
= 1500 N.
882 N / um rigidity.

The best machine tools might do 30-100 N/um, or 8-24x worse.
Iirc the industrial criteria for VMCs == 30N/um... on textbooks.