I like the Barnes 127LRX for hunting, the rest of the year I shoot traditional cup and core bullets like Hornady ELD and the Barnes Match Burners.
I have experienced the same issue switching back and forth. I can shoot Barnes copper, then switch to lead core bullets, and it settles down in a couple shots and shoots great. But if I go the other way and switch back to Barnes copper, it shoots them like crap, never settles down until I clean the barrel and start fresh. Same results across 3 different rifles here. 2 Tikkas and a Winchester.
I don't know why this is, but I do know that Barnes monos are made from 99.999% copper wire, and the gilding metal that traditional copper jackets are drawn from is an alloy of mostly copper with some amount (roughly 5%) of zinc, to soften it and make it easier to draw.