The power savings are nothing short of significant. The previous generation Apple TV wasn’t really a power hog, with platform power maxing out at around 1.6W, but the new model tops out at just a watt. Overall the power savings seem to be around 800mW across the board.
Since there is not a change to the process technology, it appears the reduction in power consumption is from other architectural or silicon optimizations.
Notably, since the Apple TV already used hardly any power there isn't much to be saved in costs.
Assuming you’re using the Apple TV for watching video 8 hours a day, every day of the year, you’d save about $0.26 per year on your power bill (assuming $0.11/kWh). You’d break even on the $99 cost of a new Apple TV in about 385 years.