This ignores the magnetic interactions though!!
The solar magnetosphere encompases the whole solar system. Exiting that magnetosphere is when you hit the heliopause, and enter interstellar space.
A black hole does not really have a magnetosphere; the necessary photon-photon interactions needed to have the requisite field lines are impossible, because photons cannot escape from the blackhole's event horizon. This means that unless the hole is actively feeding (and therefor has a plasma torus surrounding it) there cannot be such a strong magnetosphere. (in either case, the hole itself cannot sustain a magnetic field. The torus just on the event horizon makes the field, driven by obscene dynamo effects.)
You should not discount the impact this would have on planetary systems. Large, highly magnetic bodies like Jupiter would become the main forces of magnetisim in the planetary system (again, unless the hole is actively feeding), and this would perturb the orbits of smaller but still magnetic bodies, like the earth.
If the hole was actively feeding, the field produced by the plasma torus would be many times stronger than that of our sun, because the excitation energy is much higher. (matter is literally being pushed up and passed the degenerate threshold at the inner side of the torus!!) This strong a field would tug on massively magnetic bodies like Jupiter, pulling them into the inner solar system.
Black hole sun would not work the same as a normal star in either case.