It may seem so at a first glance & both produce the same results.But space & time are treated equally in Heisenberg's formulation : the operators are time dependent.In Schrodinger's formulation, states are time-dependent while the hamiltonian may be time-independent. This makes the former congruous & adaptable to relativity.

Also, the initial state vector remains fixed & operators move in Heisenberg's formulation. The initial state is not of so great a consequence as in Schrodinger's picture. Hence, it is more congruous with quantum field theory .(When particle creation & annihilation is involved, we can't work with a state vector in a Hilbert space).

I wonder how the two become totally compatible in the non-relativistic formulation.