Three strands of wire will generally have more cross sectional area than two, even if they're slightly smaller in dia. so theoretically you can flow more current through a triple vs. a double...
A triple will have more Copper per turn than a double...so it also changes or it can change the Copper to Iron (of the stack ) ratio.
All of that needs to be balanced by the strength of the magnets...the timing, etc. etc.



It's hard to say really if a triple will work better than a double or single, because there are a lot of variables involved.