There is probably some difference in mechanical advantage, whether from the design of the callipers or the different slot heights of the respective brake pads. A clue is in the pad clearance at the rim, greater clearance suggesting weaker braking.
Flex in the brake arms should not affect braking force directly but would affect lever travel and feel.
Friction in the entire system from lever to calliper is important but friction in the calliper pivots especially so. When the brakes are applied the pads tend to be dragged around the rim. This creates a strong reaction load in the pivots, greatly increasing pivot friction compared to friction when the wheel is stopped (i.e. the friction you experience when you pump the brake lever, even hard, while stopped).
This pivot friction (stiction) ultimately limits the braking force you can apply. Its effect on braking varies greatly with pivot bearing quality (hence expensive callipers ‘mysteriously’ working better despite equal mechanical advantage) and also with the distance between the pivots and the rim (unequal in dual-pivot callipers and longer in long-reach callipers). It is also the secret of the V-brake’s stopping power: the short distance from pivot to rim reduces the effect of pivot stiction, converting more of your lever force to pad force while the wheel is turning.
I would try different pads, maybe Kool Stop. Then new cables and housings of known quality. Then, if braking is still bad, replace the long-drop calliper with a Shimano BR-R650 if it’s not already that or even Tektro/TRP’s best equivalent – I read somewhere it is even better than the BR-R650 but I forget the model name.