I hesitate to jump into this discussion for several reasons but mainly because I'm certain to offend someone. OK you guys don't be offended just take this as one persons opinion. Also not sure if you are shooting static steel or falling steel where reloads are probably required.
I started shooting revolver in a (static steel) steel league, my first year was 2015. When I started I was using a S&W 686 with a 4" barrel, 6 shot capacity, reloads using safariland comp 3 speed loaders. My performance in this local league in 2015 was similar to D.B. Cooper, always at the bottom. Although it's difficult to put this into a baseline score because every match was set up differently, there is always 5 targets including a stop plate, 5 strings per stage, 5 stages per match, throw out the worse string in each stage, minimum 125 shots, after the throw-outs 100 shots count. Sort of the same as steel challenge except always 5 stages per match and the stages are wildcats. The league is similar to steel challenge.
So again there usually are about 20 revolver shooters more or less so it's isn't just me against the bottom feeders. First year I averaged a time of roughly 270 seconds. I actually didn't finish last for the year, rather second to last LOL! Second year (2016) I averaged again give or take about 160 seconds, last year 105 seconds and this year I'm running in the low to mid 80s +/-. Also, last year I started shooting Steel Challenge optical sight revolver. First 8 stage match shoot 266 seconds (classified D), I was just this week re-classified to A, I'm running about the high 130s. In Steel Challenge iron sight I'm classified B, I will shoot about 165 at this juncture. My point in all of this is I have been the goat and suffered maximum humiliation but have made (in my opinion) a lot of progress. This is for me been a 3+ year struggle. So, I'm not a Master but I know a few things about this.
There are a couple of truths that have to be brought out and this is where I'm going to insult someone or something. First thing is practice. As others have posted you must dryfire often and use a shot timer with a par feature. If, as another poster mentioned, if you lose 1/2 second on your draw that is a gain of 2 seconds per stage, 10 seconds/match in a 5 stage match. Your draw needs to be about 1.5 seconds or better.
Revolver has the disadvantage of a long heavy double action trigger. It sort of makes up for that in that you can load as light a load as you want. My loads are close to rimfire, all you need to do is get the bullet to exit the muzzle, you are not cycling a slide. Take advantage of that. Of course if you are shooting plate racks or falling steel then you need something with a bit more ommph.
In theory there is nothing wrong with 44 magnum. The real problem is the number of rounds. Six is not enough. In (for example) steel challenge there is no chance of doing well, even semi-well, if you are doing reloads on the clock. There are two options, first is never miss, the second is use a revo that holds 7 or better yet 8 rounds. Even with 8 rounds in the cylinder, the goal is to have 1 shot, 1 hit. For every miss figure an extra second added to the score. So to be clear on this accuracy is vital but having the extra rounds is useful. All of the top steel challenge revolver shooters use 8 round revolvers. There are no exceptions that I'm aware of. So, the discussion about moon clips vs. speed loaders is irrelevant because as mentioned reloads on the clock are death. My first year I was doing many on the clock reloads, So far this year I have done 1 on the clock reload and that is 1 too many but things don't always go as planned.
I have shot with guys that have 6 shot 625s and never miss but I can usually beat them because I have some extra rounds for make up shots. I see no advantage in a 625 over a 44 magnum or .357 686 (if they are cut for moons) because again, while a 625 with moons is faster to reload you simply don't want to reload.
Lets say you have a wall of steel in your league. Suppose there are 30 or 40 falling steel plates. There you have to reload, even the auto-loaders have to. But with 8 shots on a 40 plate stage you would do 5 or 6 reloads, with a 6 shot it's 7 or 8 reloads. 8 shot is the way to go.
While it is true that some of my "success" (no one is asking me yet for my autograph by the way) is due to equipment, 8 shot revolvers, dot sights (in OSR), tuned actions, chamfered charge holes, moon clips and speed holsters; practice...and a lot of it...is the main thing. I can and do shoot 6 shot in IDPA and ICORE limited 6 or Classic with speed loaders but when it's time for seriousness out comes the 8 shot.
One last thing, one of the best reloaders using speed loaders is Josh Lentz, there are a number of you tubes of his reloads if you are interested in further study on the subject. Josh uses Safariland comp 3s. There are several companies that make speed loader belt pouches.
Some will say the object here is to get practice with the revolver you carry. I get that, I really do. However, that doesn't change the fact that if you desire to run with the other shooters you have to have tackle that will give yourself a fighting chance. That or convince yourself that there is a certain noble quality in shooting a 6 shot revolver and coming in last. Again not to insult anyone but there it is. It is possible with the right gear and more importantly a lot of practice for a revolver to keep up with the semi-auto shooters. Even at my puny level of marksmenship last week I finished 2nd in a 6 stage steel challenge match in what is called the "main match". This comprises those who shoot all centerfire handguns drawing from a holster. To get 2nd I had to do better than a bunch of open auto and production semi- auto shooters. And I'm basically a piker.