To elaborate a bit on B2N2...
On the 757/767, the RAT is intended for a dual engine power loss - and only provides hydraulic power (and a limited amount of that). Even at max cruise altitude, if you lose both engines (and can't get them restarted), you're going to be on the ground in less than 30 minutes (rule of thumb - engine loss at cruise gets you ~100 miles and ~25 minutes endurance). The 757/767 has a backup battery good for 30 minutes - so (assuming a healthy battery), you'll be on the ground one way or another before the battery dies. The HMG (Hydro-Mechanical Generator) can provide sufficient electrical power to fly the aircraft if you lose all electrical generation, but at least one engine is still running (hence its need for ETOPS).
The 777 - being more electric and FBW - a 30 minute battery simply wasn't practical. So the RAT drives both a hydraulic pump and a generator to meet that 30 minutes after a dual engine power loss event.
I assume the 787 is the same as the 777, but no first-hand knowledge.