At every level of playing strength there is something specific that makes the difference. Chess skills tend to develop not always simultaneously but rather in steps one after another and then from the first theme (but at a higher level) on again, and that is connected with both their comprehensiveness or ease to grasp and their effectiveness (how much they influence one's games).
A beginner will win more often because of a slightly better ability not to hang material. For him book opening knowledge has no significance whatsoever because any advantage gained in the opening is negligible to the effect of a subsequent mistake. A master will, quite contrary, win more often because of that same better opening preparation possible and also independent on the exact proportion of his calculation acuteness to that of his opponent - because at that level mistakes are reduced a great deal anyway and aren't so decisive, while there's much more sustainability of middlegame play quality so that the opening variation (and preparation therefor) matters. Also more obvious deficiencies of one's game are easier to notice and change, hence their correction is usually preferred to devoting time to more intricate matters, and it subsequently improves one's play to a better state than his opponents' and makes one a better player.
The same can be said about any two tangibly different levels of playing strength. Moreover one tends to benefit more from having well-rounded abilities according to his overall performance quality than from one outstanding skill at the expense of others. So there's no single answer, or rather the answer depends on the player - on his general playing strength and on his particular skills.
Agree mostly, but reaching master level can be quite hard but can still be outplayed because they make a series of mini-mistakes that aren't even worthy of a ?! mark individually. For example a 2300 converts a superior initiative into a positional weakness because the opponent is forced to defend making concessions. The opponent lacks the initiative and made concessions to avert mate or material loss, but with best play would still draw a tough game, but makes suboptimal moves, loses a pawn, and the winner wins a tough technical rook and pawn ending.
I like the picture by the way, Topalov had an amazing performance at San Luis 2005.
1.Study
2.Talent
3.The drive to better onesself at the game.