Xbox One runs quieter during gaming:
Idle: Xbox One - 42dB, PS4 - 42dB
Blu-Ray: Xbox One - 43dB, PS4 - 42dB
Gaming: Xbox One - 42dB, PS4 - 51dB
Xbox One draws less power (except in Standby-Mode):
Idle: Xbox One - 65W, PS4 - 80W
Blu-Ray: Xbox One - 77W, PS4 - 100W
Gaming: Xbox One - 125W, PS4 - 131W
Xbox One's "case"/hottest spot temperature is only higher during gaming (PS4 vent peaks at 50°C)
Idle: Xbox One - 35°C, PS4 - 40°C
Blu-Ray: Xbox One - 37°C, PS4 - 41°C
Gaming: Xbox One - 49°C, PS4 - 44°C
From Digital Foundry's "Hardware Test".
I'm kinda sceptical about the cold boot, wouldn't that be longer than the 360?