So I do apologize if this has been brought up in the pages before, but here it goes anyway.
For the sake of argument, let's assume two basic groups for the game; that is a mid-to high-handicapper's mental game vs a low-to-scratch handicapper's mentality. They are pretty diverse groups, with a large span in between each group (20 HC and 10 HC are both considered mid to high, and 5 and scratch are both low and scratch), so it's intentionally broad in scope.
The key to understanding the balance between the short and long game is to summarize the goal of good golf; creating opportunity.
I've read on this website somewhere that the difference between a 20 HC and a 10 HC is closer than the difference between the 5 HC and the scratch. This is probably because as a 10 HC player, you make generally fewer mistakes than the 20 HC player, but they are similar in nature (mental errors are fewer but not extinct; basic form issues are minimized (OTT-like issues); and our misses on the green are similar (putts are generally a similar distance away, with a larger percentage of the 10 HC player's wedge shots getting closer than the 20 HC player)). 10 HC players also have a larger arsenal of recovery shots in their toolbox; I know it took me forever to pull off a good punch shot from under the trees, and now it's a good go-to shot based on the conditions. But IN GENERAL, there are more similarities than differences between the 10 and 20 HC player. A similarity is that the long game is generally not as consistent (not good or bad, but consistent) with the mid to high HC players. Drives are not always in the fairway; hybrid and FW shots are not always laid up well; sometimes you're playing from the rough more often than not; etc. These are generally lost shots; it's difficult to consistently make par from these areas. You don't create opportunity when you slice every other hole, you are fighting the course. The Best way, not the easiest, or the fastest, but the best way, is to get the ball on the fairway. The only way you're keeping the ball on the fairway is by keeping it in play off the tee. So generally, the best way to create opportunities to score well for the high handicapper is to keep the ball in play off the tee, or the long game.
Low to scratch players, on the other hand, are worlds apart in how consistently they score, and this is because of their short game. They need to hone their short game because the more precise they are, the better they score. They have fundamentals ingrained deeply to the point where it is reactive in nature; they (unlike mid-to high HC players) don't think about everything during a swing, only what is necessary to place the idea of a good swing in their head. I swing my best when I minimize the junk in my head to a simple idea (Ex. Hit the green, strike the tangent of the ball, short follow-through, etc), and just execute that simple idea. In other words, the facets of the game are generally covered well with low to scratch players. In this case, consistent accuracy, not just consistency, is a premium. They are already creating opportunity with their long games more consistently than the high handicapper. A scratch player can get it on the green with eyes closed; how close they need to get it, controlling the spin, understanding the grain of the grass; these are all factors that come when you know you're getting on the green. You know you're getting on the green, as a scratch player, when you are at 130 yards in the fairway with a wedge in hand. The question becomes how to do it on this particular hole; hop and stop, bump and run, or spin it back? These questions are set up by your long game, which is already solid. It's your short game that matters more at this point.
And amac is right; none of it matters if you get so angry after every miss that you break your clubs in half. Mental discipline was one of the hardest but most valuable lessons I have taught myself. It is vital to keep mental mistakes at bay, to accept your mistakes, and to be able to move on.
Those that say the long game is best but don't produce when it comes time to put the ball close need to work on their short games. Those that say "Drive for show, putt for dough"; a one-put for a bogie is worse than a two-putt for par. You should've probably driven the ball better to set you up for that one-putt birdie. It goes hand in hand; they are always dependent on each other. Many of you guys have said this in one form or another. The scratch player doesn't neglect his or her long game after they get to scratch, and the high handicapper doesn't forgo the short game because they are a 20 handicapper. It's a continuum, which is probably always changing and moving throughout a golfing career. But in general, it is probably better to work on getting consistency in the long game so that opportunities are created for the short game.