What you call the "Power Jibe" we call the "Step Jibe" because you step before or during the sail change. What you call a "Speed Jibe" we call a "Carve Jibe" where you switch feet after the sail flip.
A Power/Step jibe is harder to learn but has more applications because you are forward on the board when you flip the sail so if you loose speed for any reason you still can keep the board flat and stop it from rounding up. In a Speed/Carve jibe if you loose speed you are toast because you are standing on the tail of the board when you flip the sail as you have seen. That is why all racers use a Power/Step jibe for racing. The Speed/Carve jibe is more commonly used with smaller gear and in higher winds where it is easier to keep the board on a plane.