For those thinking about stiffening or modifying a cage, the most important factors are:
1. Tube diameter (not material, or wall thickness). Even adding 1/4" has a huge effect, far more than a direct comparison of new vs. old. Example, other variable removed: replacing a 1-3/4" tube with 2" (only 1/8" less space around it, and 1/8" closer to the interior), which looks like +14.3%, instead adds 53% to the bending resistance (and only 15% to the weight).
2. The longest unsupported tube length (between points of attachment with no intersections). Length is the enemy of stiffness, a 4' tube divided into 2 each 2' tubes (make triangles) is a 700% improvement. Even attaching a strut close to one end (making 1 piece 1' and the other 3') adds 137%.