In the US, both of these are commonly used. I use them interchangeably, the same as most others I know. :)

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.

For me, they have the same meaning, but "blackout" seems more informal. However, I see "outage" more frequently than I used to.

Thank you Anthony! :)

They are basically the same used synonymous, and both are very commonly used so it really just depends on the person. Although I will say that a "blackout" kind of has a sense of affecting a large area and not just a single house.