Newtonian as well as special relativistic dynamics are used to study the stability of orbits of a test particle moving around a black hole with a dipolar halo. The black hole is modeled by either the usual monopole potential or the Paczyriki-Wiita pseudo-Newtonian potential. The full general relativistic similar case is also considered. The Poincare section method and the Lyapunov characteristic exponents show that the orbits for the pseudo-Newtonian potential models are more unstable than the corresponding general relativistic geodesics.3682716720