Minerva was fired towards the asteroid by Hayabusa, but it did not have its own propulsion system. The problem was that Minerva was released at the wrong moment:
While awaiting the ground command to deploy MINERVA, the Hayabusa mothership was under autopilot control to maintain a set distance above the surface. As it drifted up or down to a range limit, Hayabusa fired small gas thrusters to stay within the designated interval.
According to Kawaguchi, the deployment command happened to arrive at Itokawa during a period when Hayabusa was drifting away from the surface. Since the escape velocity associated with the asteroid's faint gravitational pull is so small — about one-half of a mile per hour (20 centimeters per second) — MINERVA was sent on a flight path that took it away from the asteroid.
Philae, on the other hand, has its own propulsion system. The Active Descent System is a cold-gas thruster. This can be used during the descent, and it is used after landing to make sure that Philae doesn't bounce off. The lander also has shock absorbers on its landing legs. During the landing, threaded spikes are extended from the landing legs to screw the legs to the surface.
After the landing, a harpoon is fired into the ground, again to hold the lander down. Philae contains cameras that will start imaging the landing site before touchdown, so ESA can compare before and after and detect any damage to the landing area.
Video explanation using a Lego model of Philae.