They're interchangeable. I guess I am more likely to say "power outage" for something that affects a small local area. If a transformer on a utility pole blows and takes out a few blocks, when I call the light department I'd probably say "my power is out" or "we're having a power outage."
"Blackout" suggests a big event. For example, I still bore people with stories about the great Northeast [U.S.] blackout of 1965. There we were, in Cambridge Massachusetts, sitting in darkness in the dormitory cafeteria listening to our battery-powered radios... able to pick up Canada because all the nearby U.S. radio stations were out... and listening to a Canadian newscaster saying "rumors that the blackout extends as far south as Boston have not been confirmed."
P.S. The word "blackout" has many other meanings, however. It can mean a momentary loss of consciousness: "The fighter pilots wore G-suits so that they wouldn't have blackouts in tight turns." It can mean a prohibition on broadcasting sports games: "The local games are blacked out." It can mean carefully blocking a window with lightproof material, originally to prevent light from escaping as a defense against air raids.