I checked more advanced options. There is an option to reduce the minimum processor state when unplugged. I set it to be the same as when plugged... and the same happens.
I didn't see any more relevant options that were different.
Using power save mode, plugged, gets 60 FPS.
As for the laptop I am testing, it is from last year. It has an Intel core i7 2.5Gh. I think it might have 2 graphic cards, an Intel and a nVidia.