The Mk II or Mk III will be more accurate by far. There may be an exceptional Single Six in someone's possession that will match the average run of the mill Mk II/IIIbut you'd have to look far and wide to find it.
Having owned a bunch of Mk II's over the years I had a very strong prejudice against the Mk III until I bought one. The loaded chamber indicator is hokey and Ruger loves to make them oversize on all of their pistols that have one. The mag safety is superfluous IMO but the Browning Buckmark and Hi-Power both have them and that doesn't seem to stop people from buying those. It can always be disabled.
On the good side - I really like the magazine release by the trigger where it should be, it's much more instinctive when switching between the Ruger and my other semi-autos. I like the drilled and tapped receiver and Weaver base supplied with the pistol, that makes it easy to put a red dot or scope on it if you want to.
And despite the added "features", it's still the same basic pistol Bill Ruger first made over 60 years ago, and still just as reliable and accurate as ever.
+1
