The differences has to do with design, materials and manufacturing tolerances. Nicer V-brakes have better materials & finish and will typically last longer. They'll be easier to adjust and service. However, braking-power may not be that different since ultimately, it's the friction between the pads and rims that translates into friction between the front-tyre and ground that determines your deceleration.

Cables have negligible stretch under load, it's the brake's arms that bend. Better designs are stiffer. Another cause of flex is the fork itself where the mounting posts are forced apart. A brake-bridge brace will stiffen that up nicely. Also cable-friction can rob A TONNE of braking-power, make sure your cables slide easily in their housings. I like the cables that have the inner-wire drawn through a die so that the outer surface is perfectly smooth.

Another cause of V-brake issues is that the levers aren't matched to the brakes. However, in your case, if you have non-compatible levers (non linear-pull), you'll actually end up with MORE mechanical leverage and single-finger lock-up power from the brakes.

I'd go with the KoolStop pads first and replace the cables if necessary.