This is a very tough question because you need both almost equally to win a cup.
Nashville is an interesting case where you look at them and they were not that good of a team team a couple years ago but then the GM made some savvy moves and aquired guys like Subban, Turris, Johansen, Forsberg, and now they are one of the very best teams.
You look at Edmonton, they have a great foundation, they look to be like one of the best teams in the league going forward and the GM makes some terrible moves. They trade Hall, Eberle for bad returns, trade the Barzal pick for Reinhart, sign Lucic and Sekera both overpaid. Had the GM been Poile instead of Chiarelli, that team is one of the best teams in the league today if not the best.
You need the GM because even if you have the best player, there's no way you win without a smart GM. You need a GM that can acquire players that will make a great team surrounding that star player. But you also need that star player. (Kane, Crosby, Kopitar/Doughty, Ovechkin) The competition is stiff in this league. You need top 5 GM and top 5 player at his position (F or D) to even have a chance at the cup.
However, I would choose GM over player because if you have a smart GM, your team will be competitive all the time even if you don't win the cup. Having the best player doesn't mean you'll be competitive.