The most important factors to a large extent depend on the discipline in which you compete. They are not necessarily the same and therefore different factors may be weighed more heavily in one discipline versus another.
In F-Class, we shoot long strings of fire (20+ shots) over a period of anywhere from 5 or 6 minutes, to as long as 20 minutes. Wind changes during that time period are what will cost you by far the most points if you miss them. A rifle that will shoot 0.25 MOA 5-shot groups at 100 yd should be capable of producing 20-shot groups in dead calm to very benign wind conditions in the 0.50 to maybe 0.75 MOA range at 600 yd, and perhaps slightly larger at 1000 yd. Because the F-Class target "10-" and "X-" scoring rings are 1.0 MOA and 0.50 MOA, respectively, that level of precision is readily capable of producing cleans with high X-counts in benign conditions. Depending on the cartridge, even a 1 or 2 mph wind is enough to put a shot out of the 10-ring at 600 yd. Wind values between 5 and 10 mph can easily put a shot off the target face without correcting for the wind effect. Thus, spending days/weeks/months trying to tune a 0.25 MOA load into one that shoots in the 0.1s or better is going to do very little in terms of improving your scores when the wind conditions are challenging. You're talking about a difference between something like 0.1 to 0.2 MOA improvement at the target face (load development) and an effect that can easily put your shot out into the 8-ring, 7-ring, or sometimes even off the target face (missed wind call).
For F-Class, having a rifle setup that can consistently shoot groups at 100 yd under 0.5 MOA is sufficient to be competitive at the local, state, or perhaps even regional level. One that consistently shoots 0.25 MOA is even better. When you start talking about hummer barrels and the most expensive reloading equipment, there is no doubt they can also have a beneficial effect. But that effect is more readily observed among the very top shooters; i.e. those that already have very good wind reading skills. Certainly such things can make a difference amongst the top shooters, where even a point or two, or a slightly higher X-count means the difference between winning and not winning. At the very top of the leaderboard, it's different ballgame where EVERYTHING matters. So the answer to your question also depends to some extent on the definition of "competitive". One thing is certain, having a hummer barrel or that load that has been tuned to gnat's whisker is not going to allow someone with poor wind reading ability to win big matches, not even close.
The debate over custom versus factory rifles would be better answered by simply asking to what level of precision a given rifle will shoot. I've seen a factory rifle or two that would shoot extremely well, although most are mediocre. I've seen upgraded "factory" rifles (i.e. trued, with a quality aftermarket barrel) that were very competitive. I've also seen a few custom rifles that frankly didn't shoot all that well. Regardless of its origin, the level of precision to which a given rifle can shoot is the best measure of its potential. Also regardless of the origin of any given rifle, the difference between commercial ammunition and handloads can be substantial. With commercial ammo, the best you can do is test as many as possible and find the one your rifle shoots best. In contrast, handloads are specifically tuned to the rifle. In addition, the variance (i.e. charge weight, seating depth, etc.) between loaded rounds produced by a competent reloader and those manufactured by a machine are night and day. Even the most expensive commercial ammunition typically has significant variance in charge weight and seating depth that no competent reloader would ever accept. Finally, reloading allows one to choose bullets with the highest possible BC, the best precision, the best uniformity, so on and so forth. In most cases, the "best" bullets for a given discipline are not even available loaded in commercial ammo, so if you don't roll your own, you're simply not using the best bullets available. Collectively, all these things can certainly make a difference. But as I mentioned previously, putting a top quality custom rifle and finely tuned handload into the hands of a novice windreader is not going to allow that person to win big matches in F-Class. Not even close. So the big picture is one where you use the best equipment you can realistically afford, then you do whatever it takes to hone your windreading skills, as well as those in other critical areas.
