The powder load with the SWCs makes that load pretty light, which helps with accuracy. I used to load wadcutters with about that and got extremely comfortable one-hand shooting loads that were perfect for trigger practice.
The plated bullets are an unknown quantity, since you don't say whose plated bullets you used. It doesn't take a huge investment to set up to plate bullets, but some manufacturers are much better at making consistent, reliable plated bullets than others. So some of your modestly lesser accuracy could have come from the bullets themselves being less consistent.
Further, the load you used wasn't even as "hot," as the SWC load. Some bullets need a minimum velocity to stay stable, and that's possibly the most important variable in this comparison. Alliant's site shows a recommended load of 4.5gr of Bullseye behind 125gr bullets, while they recommend 3.5gr behind 158gr SWCs; your chosen load was lighter than their recommendation for the 125gr but hotter than their recommendation for 158gr SWCs.
I know that "plated bullets are supposed to be loaded more like lead bullets," but at the end of the .38 SPL velocity spectrum we're talking about, there is no real difference; those are all essentially lead bullet loads. So while your results were not as good with your plated bullets as with your lead SWCs, they weren't too shabby to start with, and while you worked up the loads appropriately, there are a few variables you didn't control for.
Finally, as others have mentioned, I'm not keen on your testing method. It's better to run all of one type of load, then all of the next, then...etc. rather than alternating between different loads for a number of reasons. Anticipation, more than anything else, can cause both/all of your loads to look poorer than they might. And you want to also consider a light field cleaning between different loads, both to allow the shooter to rest between loads and to have the gun as close to the same as possible for each load you test.
In short, consistency is essential, both in loading and in testing processes. Not that you were doing precise measurements, but you could have gotten a better idea of each load's potential by using a set procedure for testing each load you test. Which, I think, is more fun anyway...