BigDog's power pack was originally a constant speed gasoline engine driving a hydraulic pump and an electrical generator. That's the noisy engine in the earlier videos. The LS3 was supposed to have a new, quieter power pack developed with a small variable-speed Diesel engine. That was subcontracted out by Boston Dynamics. This is as good as it ever got: [1] It still sounds like a dirt bike.
The hydraulic system used is very controllable but not particularly efficient. There's no energy recovery and no springyness; it's brute-force hydraulics. That was reasonable for an experimental machine, but not acceptable in the production product. Atlas, the BD humanoid, has the same problem. It's too similar to BigDog, and weighs about 330 pounds. Schaft, Google's other humanoid robotics company, uses water-cooled electric motors, like Tesla. You can enormously overload electric motors for a few seconds without hurting them, and if you have cooling and temperature monitoring, that works fine. This is probably the way forward for anything smaller than a pony.