Centered headlines give the newspaper more classic and traditional look,.
Flush left headlines are more modern and create more white on the side;
This alignment must be accompanied with other elements that have the same alignment (quotes, leads, captions under the picture, the authors of the text, etc.), while this rule does not applie to centered headings.
Flush left headlines fits more to tabloid, while the broadsheet may use any style;
Consistency is important: Let all the headlines in newspaper or magazine be flush left or centered.