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In the vertical plane, not a lot. Esp in the rear triangle where it's often said to be. But Steel bikes are more likely to have lateral twist kind of flex and that accounts for a lot more comfort and ride feel (good and bad, depends how much etc) than most give it credit for or realise. Al frames can also do this too. The Arkose was always designed and ride-checked not to be too stiff against those lateral twist forces. Eg there's a big difference in that area between an Arkose and a couple of other Al frames I've ridden - some are silly-stiff imho.
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there's a big difference in that area between an Arkose and a couple of other Al frames I've ridden
How much in actual units please? To be honest, I don't believe the difference could be detected in a proper blind user test (which admittedly is almost impossible to do).
Edit: I own a notoriously light and flexible Ti road frame, and when ridden in a turbo trainer the BB visibly moves at least 10 mm side to side. But I'm not at all sure I can genuinely detect that through displacement of my feet, and given it's clamped at the dropouts the tyre flex is removed from the problem.
I find this interesting, genuinely curious as to how much you can tell about frame material through like, 45mm of rubber. It's particularly relevant especially given the price of steel gravel bikes at the moment.