I'm going to start right off by being an obnoxious heretic and claim that the two aren't really a dichotomy. The trade-off space here is actually more complex than that.
Let's consider the following - you're a hunter, or a sniper. You chamber a round - goes in smooth, you aim, fire and miss.
Which would have been more important to "reliability" - the fact it went "bang" or the fact you missed? If a hunter, the game is now spooked, if a sniper, it's worse - the game shoots back - and now they know you're there and about where you are.
As John Plaster said - it can only raise your insurance premiums. So reliability, as usually defined is just plain wrong here - if you miss, the rest didn't matter one bit, and it could be argued that failing to chamber or just going "click" would have been a lot better outcome, eh?
Seems the usual (unsatisfying to those who like simple absolutes) answer of "it depends" now comes into play.
In a combat situation - one I've managed gratefully to miss out on myself, and hope to remain so - everyone knows you're there anyway, and even if you miss, you might get what you want out of getting them to keep their heads down - so an inaccurate but reliable fusillade of fire might do the job you need done right then. The reliability question is a lot more clear-cut in that case. Sure, you'd prefer accuracy, but when charging a position, or retreating - you may not have the luxury of taking time to aim well anyway. Plain old reliability is therefore king in some combat situations.
In match competition, you're "charged" with every shot. One that misses is also worse than one that didn't fire or wouldn't chamber. In long range accuracy games, you have plenty of time anyway, but you can't afford any "bangs" that don't result in an X ring hole. So here we are back to accuracy being the dominant desire, a malfunction that doesn't hurt anything is annoying, but that's all. Even if you have to take out the bolt and use a cleaning rod to poke out a hard to extract shell - no big deal.
It's nearly the same in handgun bullseye competition - plenty of time to aim, a misfire isn't the end of the world, usually.
In the run and gun games - ones I don't happen to play (because I stink at that and am unlikely to improve at my age) - we're back to reliability - they are a rather weak attempt to duplicate combat situations. Accuracy isn't so important, ranges are short, and it'd be hard to convince me the winners spend much time aiming anyway - at most it looks like muscle memory and fat forearms to control guns in recoil to get another shot off quickly - time is score.
Now, as it turns out, as classically defined, there IS a trade-off. The very most accurate ammo has a tendency to be a tight fit (just a tiny error in building it and it won't chamber - or will fail to extract), lack the ability to take abuse in something like a slam-feed autoloader (or just rough handling on the way to the match), and probably doesn't "keep" as long in nasty conditions, as we in this case do care about things like bullet-case neck friction and cold welding, straightness and uniformity. You can't really get away with crimping and sealing match grade accurate ammo against the weather, either, it makes it non uniform, and leaves crud in the gun that can affect the accuracy of later shots.
Self defense is it's own unique issue(s). There, you should really use factory ammo for a bunch of legal reasons. You might be committing a homicide - or close (which can be worse, now you've got a crook on the other side of a courtroom, probably a much better liar than you are, with all that implies). You sure wouldn't want to wind up in court explaining to a lawyer on the other side why you were crafting "especially deadly or brutal wounding" ammo - you know the other side is going to spin it that way, even if your self-defense weapon is a snubbie with a light, target hand-load in it. In this case, you need a bang and a hit, both, at least as well as can be managed in a horrible situation you're never going to be used to - you'll be overcoming adrenalin and fear while trying to shoot in bad conditions, quickly. There are other esoteric issues as well. Since it's a very commonly held "urban myth" that say, a .38 isn't that good for this job - cops tell endless stories of perps continuing to keep coming after multiple hits - it might actually be a better carry weapon (since almost everyone shoots better than most cops - you do have to point the thing in the right direction, something that seems to be lost on many), than say a .45 ACP, which "everyone knows" is a fight stopper even if you just wing the guy. You'd not get as much crap for emptying a .38...which is sure to do the job. Some legal theorists claim that it's definitely better to kill the guy in these cases - I have no experience and don't wish to collect any. At any rate, self defense that works is homicide in most cases where shots are fired (there are significant cases - more than when shots are fired - where the perp just runs away when he sees that gun or laser dot). To use that "defense" you have to admit you shot someone - now you have to prove it was justified, which the theorists claim is going to be easier if you're the only one with a story to tell afterwards.
I don't claim to have the ultimate insight here, this is just one of those things that got under my skin a little - as if there were one or the other, when in fact, it's obviously a continuum, depending on need and use. So I'd like to hear anyone else's comments on this. There ARE trade-offs in ammo design and construction here - not as bad as it used to be - quality parts can be pretty good at both metrics, but...
Discuss!