I have two, one of which is the birdshead model, with the 3.5" barrel. They're both fun little plinkers, hard to put down once in hand. I got them both long before the Wrangler came out.
I also own a NM Single Six. The quality difference is evident, but so is the difference in price, and I'm not sure they're commensurate with one another.
With the Wrangler, which is now available also in a birdshead setup, you get:
The Ruger name, a better aluminum frame, real transfer-bar safety, weird Cerakote colors, and cheesy plastic stocks.
With the Heritage, you get:
A zinc-alloy frame, a goofy manual safety (that allows dry-fire), blued-steel cylinder and barrel, more-"authentic" colors, an optional .22WMR cylinder, and real wood stocks.
The Wrangler runs $45-60 or so more than the HRR does if the HRR includes the Magnum cylinder, and more if the HRR does not.
I put a few rounds through the Magnum cylinder in the 4.75" one when I got it, but have no real use for that loadup in that gun, especially since I've since acquired a different revolver chambered for .22WMR. I don't see much point in Magnum in the .22 SA revolvers in this price point.
If I was hopping for my first SA .22 today, I'd still get the HRR only because those Wrangler finishes and colors just don't do it for me.