They both are correct. However, they refer to two different ratings. Let me explain.
First, the 150W that is printed on the rear panel refers to the power consumption of the subwoofer. The 220W rating refers to the maximum power output of the subwoofer. This is the amount of power that is being used to reproduce low frequency audio by driving the speaker housed within the subwoofer cabinet. Its this 220-Watt number thats responsible for the thundering bass you hear from your favorite action movies.
Note that this FAQ refers specifically to the HT-S770/777 Home Theater Systems. However, the concept applies to all powered subwoofers that are sold separately and as part of a system.