Well, maybe I said that wrong. It doesn't make the engine any more powerful, it just keeps it in a lower gear for longer, and drops into a lower gear more easily.
Aside from the idle test, the other place you will see the power button do anything is when you're on the highway, climbing up hill. If you punch the power button then, the transmission will drop into a lower gear. If you turn the switch off, it will drop back into high.
When power mode is off, the shift points are too conservative, in my not-so-humble opinion -- especially at highway speeds. You really have to stomp on the pedal to get it to downshift. So, I usually drive with power mode on. I like it to just GO when I press the gas. I don't want it to sit there and ponder.
No power button:
"Go!"
"Give me a second...I'm sure I can get an extra 5MPH from this gear..."
"Yeah, but it'll take you a half mile and the better part of a minute! I need to pass this guy NOW, before I get blocked by the guy with six tons of hay on the trailer!"
"Okay, okay, I suppose I'll drop into passing gear..."
Power button:
"Go!"
"Gone."