The Bisley .22 is the same gun as the Single Six, just a different grip frame and hammer.
The number one reason you'd want a Bisley .22 over a Single Six is to act as an understudy to a centerfire Ruger Bisley SA. The number two reason is, you've got big hands
or detest the "pinkie under" style of holding/shooting standard-type Colt SAA or similar grips (pinkie slung "under" the grip frame).
If your bigger Ruger SA is going to have normal grips, then get the same on the Single Six.
The Bisley grip frame is noted for coping with big recoil - a non-issue on the .22 but it comes into it's own with heavy 44Mag and higher horsepower levels. The Bisley grip frame (if it fits your hand and shooting style) will make the hottest 357Mags seem downright tame. When John Linebaugh builds you a 475 or 500 handcannon the only grip frame he'll set it up with is a Bisley, for safety reasons.
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Accuracy on the Single Six is unaffected by the grip frame or hammer type. Accuracy is usually at least "decent" but is sometimes hit-or-miss. The "miss" guns can usually be spotted via The Checkout but if not, modest gunsmithing, tightening the action and a re-crown job often helps a lot. Durability is outstanding. Accuracy is almost always better than the "Heritage" cheapo rimfire SAs (with the funky safety switch to the left of the hammer).
S&W DAs are admittedly often more accurate by a bit. But they're not as cool
, they're not dual-caliber (the .22Mag is damned useful!) and worst case the Ruger will respond to minor tuning.
Again: this is all independent of which Ruger grip frame setup you choose.