Answer
Planck’s constant h would be much greater than its present value.
Work Step by Step
The size of a quantum of light energy is hf. If photons were to become very energetic, that would be akin to taking the limit as h became very large. In the same way, the de Broglie wavelength of massive particles, h/p, would also grow. The uncertainty principle (page 593) would also start to inhibit our everyday measurements.
In short, in a world with dominant quantum effects, Planck’s constant h would be much greater. A delightful book called "The New World of Mr. Tompkins" describes such a world. It is part of a 4-book series by the late renowned physicist, George Gamow.