Energy is relative, both in Relativity and in Newtonian mechanics. This means that different reference frames will determine different values for the energy of a given object at a given point in space and time. However, the conservation of energy holds in any reference frame. This means that, in a single reference frame the total energy (KE + PE) will be constant over time.
This is the difference between the concepts of "invariant" and "conserved". Energy is conserved, but not invariant.