I don't know what happened in this regard between CS5 and CS6. But your examples appear to be the natural result of working very low-resolution with no anti-aliasing. There are only so many places Photohop can place a non-anti-aliased pixel, given the very few choices it has in such a low resolution document.
As an experiment, try Edit>Stroke, with a single pixel on the path center (or its selection), and see if you like what it does. The only real difference will be that your stroke will be anti-aliased.
Alternatively, try increasing your document resolution, if your project allows.
If a path is in precisely the same location in CS5 and CS6 then strokes made with the Pencil will be almost (or possibly actually) identical in both versions. However, CS6 has an added preference to restrict the positioning of paths with respect to the pixel grid and I think that the positioning of your paths is not as you intended. You'd have got reasonably symmetrical Pencil-stroked circles if the N, E, S and W points of the circular paths lay mid-pixel. These points in your example are lying on pixel boundaries, hence the asymmetrical strokes.
To get CS5's free positioning of paths in CS6, disable Preferences > General > Snap Vector Tools and Transforms to Pixel Grid. Then it'll be possible to get in CS6 the result that you got in CS5.