For one thing, it would be hugely more unlikely to exist. We are more likely to have worlds where there is a little more deuterium in the hydrogen, not 100%.
Most of the hydrogen in our Universe is protium (hydrogen-1) because the vast majority of unfused nuclear particles in stars are protons. Neutrons must either fuse with something or they decay to make protons with a half-life of ten minutes. Deuterium and tritium are formed initially when the protons are fused, but they are just intermediate towards the formation of more stable helium-4 nuclei (alpha particles) and so do not accumulate to large concentrations.
If there were a heavy water world, life would have to adapt to it. Prolonged consumption of pure heavy water is deadly to life on Earth.