Also, the three factors lee mentions--maturity, knowledge, and experience--are very subjective to the individual.
"Maturity" is a rather nebulous term that can mean different things in different contexts, and isn't always an advantage in every possible situation.
"Knowledge" is very relative, because different people acquire different types of knowledge at different points in their lives, under different circumstances, and there will be people of varying age groups with different levels of knowledge--including very young people who will gain knowledge of certain things at an earlier age than some people decades older. It makes no logical sense to always assume that the older someone is, the more knowledge in all things they will automatically have over any person who is much younger. There are just too many possible factors to consider that work against making such sweeping assumptions due to a single point as arbitrary as chronological age.
"Experience" too is very relative, because there is a huge difference between the mere quantity of experience and the sheer quality of it, as this will necessarily greatly differ from person to person, and vary amongst all the age groups. Further, our culture attempts (with varying degrees of success) to forcibly prevent underagers from acquiring certain types of experience, and this artificially reduces both the quantity and quality of this experience, which is a game of dirty pool. That is like declaring a certain group of people to be naturally incapable of learning to read when it's illegal for anyone to teach them how to learn to read, or for them to attempt to learn to read themselves.
As for "power," if an adult has a relationship with an underager today, the latter can destroy the older person's life with a mere accusation. So who truly has the power in such relationships? Also, those we are attracted to on a deep level will have a great degree of potential control over us, and you often see adult lovers go out of their way to please their much younger lovers and to keep their favor. Since sex appeal and the powerful emotions that come with it carry so much potential to control a smitten lover, is it truly the adult who has the power in such situations, or the girl? Finally, if I am not the parent, teacher, or coach, etc., of a hypothetical AG lover, how exactly do I have power over her, especially with all of the above factors considered? Many will make the tired old claim that underagers are naturally submissive to adults, or that she will give me sexual favors to retain my friendship against her actual desires, while conveniently overlooking the fact that underage people routinely defy adult authority, and are notorious for showing extreme resistance against doing anything they do not truly want to do.