There is an important lesson to be learned from you question. The lesson is about "limiting sources of error". Limiting (or largest) sources of error are the ones that have to be addressed first, as other smaller sources of error will not have nearly the effect on the final outcome. Even cumulatively, relatively small sources of error may not equal a single larger, or limiting, source of error. So the real question here is what are your limiting sources of error in terms of precision?
My suggestion would be to start by shooting the best single target you can with the same number of shots you intend to shoot at the individual targets (i.e. a 10-shot group) using the current load. A 10-shot group makes it easier to visualize the inherent overall precision of the rifle and load; i.e. you're measuring the spread of a single 10-shot group and using that MOA/precision value to make an estimate of how it should place 10 individual shots on 10 individual targets if fired with equal precision. Shooting a single 10-shot group might actually overestimate the inherent precision a little bit relative to 10 single shots on different targets, as you can maintain position and shoot all 10 shots at the same target, rather than having to change your POA between shots. Nonetheless, it's a place to start for comparison. At that point, you can simply place the center-point of the 10-shot group at the center of the target X-ring and eyeball it. Then you can readily estimate how many of the shots in the group would have been Xs, and how many would have been outside of the X-ring on the BR target used for the individual shots.
Your description of how the load was actually worked up, and resultant precision of the load prior to switching over to the new reloading equipment is a little thin on specific details. You mentioned 0.5 MOA precision for a 5-shot group, which would be reasonable for a factory rifle with good commercial ammunition, but would typically not be in the same league as a custom rifle with a finely-tuned handload, for which I would expect at a bare minimum 0.25 MOA (or less). You didn't mention the target scoring ring dimensions, but the X-ring is actually smaller than your bullet hole. That means you have very little room for error when it comes to shooting Xs, especially if using worst-edge scoring. Without knowing with any certainty exactly what target you're using, I'm guessing you'd need a load that would shoot 0.25 MOA or better to reliably achieve a high X-count on that target, as having the shot placement move from center in any direction by only half a bullet diameter or so would put the shot out of the X-ring. For the calibers we typically see used for such purposes, half a bullet diameter will typically equate to precision in the 0.1 to 0.2 MOA range. In other words, there's simply not much room for error in precision. Shots fired in a group where the bullet holes overlapped by less than half their diameter would likely be out of the X-ring on this target. In other words, at a minimum you really want a load capable of 5-shot groups that are basically one ragged hole, which is usually somewhere around 0.25 MOA precision.
So the real question will always boil down to what is the intrinsic accuracy of the rifle/load, and of course, the shooter behind the rifle. Although I cannot tell you what the intrinsic precision of your setup from the information provided, I might be able to offer some possible explanations as to why you did not observe any apparent increase in precision after switching over to the new equipment. The most obvious explanation is that the equipment you were using previously was simply not the limiting factor in precision. In that case, switching to arguably "better" equipment would not normally be expected to improve precision, because the reloading equipment was never the limiting source of error in the precision to begin with. If 0.5 MOA precision for 5-shots at 100 yd is the best precision the rifle is capable of with that particular load, changing reloading equipment is not going to make it any better. In that event, improving the precision of the load by using a different powder/bullet/primer/brass might be possible, but you'd simply have to experiment to find out whether that is possible with the rifle setup you have.
Another possible explanation is that it always takes time to become familiar with new reloading equipment, so that you know how to get the most from it. Simply buying a new die and press and expecting an immediate improvement in precision with no other changes is not realistic, especially if the previous equipment was working adequately. I'd suggest taking a little more time using the new reloading setup, and working up the load again from scratch, with the goal of getting everything possible out of the new equipment as you are doing so. Try and see if you can't whittle the precision of the current load down a bit from 0.5 MOA to something like 0.3 MOA, 0.25 MOA, or even a bit less. Frankly, a 0.5 MOA isn't even going to be close to what you'd really like to have for a BR-style competition. Even at the local level, those folks know how to work up a load and they know how to shoot tiny, tiny groups. If you want to be in the running, you're going to need to up your game, meaning ALL of your game. That means developing a load capable of competing, which will be something much tighter than 0.5 MOA for 5-shots at 100 yd. That means working on your skills behind the rifle, so you know when there is still improvement in precision to be had from your setup with a little more load development. That means no fiddling around behind the rifle with the bag and/or shooting position when you're trying to obtain the best precision possible. These are all things you can address and possibly improve as you familiarize yourself better with the new equipment while re-working the load.
