I don't really think this is an age old question.
I think every worthwhile chess teacher in the history of the world would tell you "endgames."
Thats why I said NOT for a specific level although teachers say endgames top GM's say openings.
Studying the opening tells you what your options you may choose from. Studying the endgame tells you which of those options is best. You need both. But I prefer Lev Alburt's approach of starting players out with fewer pieces and simplier situtations that they can solve and understand definitively, and letting them work up from there.
I have a theory about the age old question which study is mor important openings or endgame and no I don't just mean for a certain level of play but just in general which study is more important. We all know that 1.d4 leads to more positional games while 1.e4 usually leads to more tactical ones. SO I played 1.e4 just off opening principles and not studying anything in depth I noticed that the endgame was usually a deciding factor of the games tournout. then I used 1.d4 but since this is my usual choice to make sure I could possibly get the same affecct i chose 1.d4 opening I have never played or rarely played just goin off of opening principles and not studying anything in depth and noticed the opening phase was usually the deciding factor in the games. SO I think the answer to this question is based off your repritore. If your more aggressive then endgame study may fit you best and if your more positional then opening study will benefit you highly but this is all still just a guess.