I'm struggling a bit with this, so I might be off, but I believe you're using the wrong formula for a tube. I believe the one you used is for a solid beam, which would be the case for the wooden bandsaw frame, not the Jet. I believe the jet would the moment of the area of the tube, which I believe is (bd^3-hk^3)/12.
https://www.engineersedge.com/calcul...re_case_10.htm
So (bd^3-hk^3)/12 = 15*(bd^3)/12
For your Jet, the area moment of Inertia works out to be:
1/8" steel: (5.5 * 3.25 ^ 3 - 5.25 * 3^3)/12 = 3.92 inches ^4.
1/4" steel: (5.5 * 3.25 ^ 3 - 5 * 2.75^3)/12 = 7 inches ^4.
So the wooden version would need to be 58.8 inches ^4 to be the match the 1/8" steel version, and 106.0 inches ^4 for 1/4" steel.
It's unclear to me how you got 1500 inches^4, seems like it should be 150 even with the simpler formula? 10.5 * 15 = 157.5 inches ^ 4
Right now, guessing from the pictures shown, I'm guessing Matthias's version is 6" x 7.5" because I think he's using unmodified dimensional lumber, and you can clearly see 4 layers in the pic.
(6 * 7.5 ^3)/12 = 210 inches^4.
So right now, it appears that his wooden bandsaw would be 2-4x stiffer than your steel Jet, using the formula for a square tube, or slightly stiffer if we use the simpler approach. Am I missing something? I'm basically learning this right now, so my assumptions could be way off.