There are certain beliefs that state that a blue moon is threefold more powerful than the full moon, although I don't follow that belief personally, as the moon is a full moon in its own time, and the only time it becomes a "blue moon" is when it is the second full moon of a calendar month. Humans made the calendar, without magical or divine inspiration, thus the only time (in my opinion) that anything has extra power on any particular day is when that day coincides with a sabbat, estbat, or the like. Our calendar doesn't hold power over the moon, sun, earth, or anything like that, and thus can't give power unto those days.
I understand that not everyone believes in this way, and that is perfectly fine. A blue moon can help someone accomplish something they normally wouldn't be able to due to the strong belief that comes with working magic on a blue moon, but the moon itself, in my opinion is indifferent as to what day of the year, month, or week it shows up on. It has been there long before we had a calendar of any sort, let alone the Gregorian calendar we use today.