The speed of impact is dependent on the large mass of the star and the small size of the radius. For neutron star of a solar mass but only 20 km across, you get a speed of impact of 110,000 km/sec, a significant fraction of the speed of light.
When you calculate the kinetic energy of a planet of say 10 Jovian masses hitting the neutron star at this relativistic speed you get about 10^44 joules. This is about as much energy as the Sun puts out in its lifetime!
Or said another way its the amount of kinetic energy put out by the supernovae itself:

Astrophysicsts receive $2 million from Department of Energy to explore supernovae.
"A supernova releases as much kinetic energy as the sun will radiate over its entire lifetime," said Rob Hoffman, of LLNL and one of the principal scientists for the project. "They are the best bang since the big one."
http://www.eurekalert.org/pub_releases/2001-08/llnl-ar082001.php

Also interesting in this article is the description of Type I supernovae (not the type that creates neutron stars.) These explosions are explained as coming from the impact of gas from a close companion star, inducing thermonuclear explosions. Then the full impact of Jovian mass planet might as well induce such explosions.

I don't know how much nuclear material would be needed to power the Mars mission for several months, but I imagine it would be several kilos. Then the concern for an accident would be many times worse than for other missions that launched with nuclear material onboard.

Bob Clark