In the case of trampolines, the spring tension is varied to give a different "feel", but the effeciency of trampolines is mostly due to the bedding material; how little energy is consumed by the bedding itself, and how little air resistance there is.
Modern day competition trampolines are 45 inches high and can handle bounce heights of about 20 feet (the head of a trampolinist can get as high a 30 feet above the floor the trampoline sits on, so minus 3.75 feet for the trampoline height and minus 6 feet for the trampolinist is about 20 feet).
There's no ideal stiffness, but having the springs a bit softer reduces the g-forces which can reduce injuries in the case of a bad landing.
Regarding balls, a superball probably takes more than 10 times a long as a billard ball to bounce, but both have a high degree of elastisity in terms of bouncing. The superball retains spin energy much better, while the billard ball is very slick and doesn't grip well.
In the case of table tennis rubber, the rules limit the rubber thickness to 4mm total. Normally the maximum thicknes is 1.5mm for the rubber, 2.5mm for the sponge. Some rubbers are only 1mm thick, but I haven't seen one that combines this with 3.0mm sponge yet.
Bottom line is stiffness or duration of collision doesn't directly correspond to elasticity.