The documentation that comes with the QuickLOAD internal ballistics program makes the interesting observation that what constitutes a magnum primer is not consistent industry-wide. Some just use more priming mix, making them hotter, while some some adjust the mix to increase flame duration and are actually milder at initial firing. This means that with a fast powder, the latter type might actually give you lower peak pressure. Unless you know your specific brand's approach to making a magnum primer, you need to assume it will raise pressure, but it isn't necessarily so, depending on what all else is in the mix. Since QL is written in Europe, I assume that description includes European brands and don't know how much of it applies to U.S. domestic brands?
In general, primer consistency is what matters most. Benchrest rifle shooters swear that having the mildest possible primer is best for accuracy, since that lets the powder charge control the peak pressure better, and the shooter is in control of the powder charge. However, that assumes relatively warm loads, good case fill, and completely prepped brass. I found, for example, that shooting Accurate 2520 in .308 I got a significant accuracy increase from using either magnum primers or by using Federal 210M (benchrest) primers but first deburring the flashhole on the inside. This was all because ball powders are harder to ignite, and that was complicated by me using a load that did not fill the case all that well.
So, bottom line for handguns, I think, is that you won't see any accuracy difference in primers except maybe in the Contender and Encore or other single-shot pistols capable of rifle-levels of precision. It seems to be the kind of difference you may see only in guns shooting under an MOA. That is exceptional for most handguns. As I said before, you do need to assume changing to a magnum primer will raise pressure until proven otherwise, so work your loads back up from 10% low, same as you would changing any other component in your load.