I've had poor performance with using 3-piece oil rings where 1-piece oil rings were, in the same pistons. With new pistons, things worked better.
But, the 3-piece oil rings don't seem to last as long (in normal use, like commuting-touring, and lots of winter neglect, like old oil sitting in the engine for long periods) as the 1-piece version, while vice-versa in racing apps with lots of redline running. The 1-piece one will let oil smoke out at redline+ speeds because there isn't enough space for the oil to collect in the rings before pushing thru the ports to the inside (to lube the rod's small end).
I've seen the 1-piece oil rings surpass 100k miles in the early engines while the 3-piece versions (which first appeared around March 1972 in the K2) have more often showed oil consumption (and weep at the head gasket) starting around 70k miles.
So, if you are using new pistons with new rings, it shouldn't matter which type. The MC and RIK rings are the best we can get right now (and my personal favorites, anyway).