Resolution will be pretty similar, that particular chip is a pretty good match for most Bayer chips of 10-12MP.
This of course is only your subjective guesstimate.
I used BartvanderWolf's excellent test chart (link earlier in this thread) to get (very) preliminary results for my Pentax K20D. This is, as said, preliminary, as I could not use a print, so I had to use computer screen instead (from far enough away with wide enough lens). The result was about 0,406 cycles per pixel. Nyquist is of course 0.5, so if we assume
that Foveon does it to Nyquist, then Foveon would do 23% better resolution than K20D (per pixel) with Bayer and anti-alias filter, thus a 4.7Mp Foveon sensor would be worth 7.1 Mp K20D sensor pixels (4.7*1.23^2).
(I must admit, that the Foveon AA-less "beyond Nyquist" false detail may also (or may not) look pretty.)
I also did a test with the color chart, and the results unsurprisingly were very similar to above, only very slightly worse. However, the computer screen isn't exactly the best choice for this test, so I'll have to redo it as well, once I get some prints (which won't be soon though, as I don't have an inkjet).
One thing that isn't talked about that much is that Foveon chip has one unique property- it has equal resolution in all colours, while Bayer resolution varies all over the place in different parts of the subject, especially in regions of saturated colour. Mike Chaney (ddisoft) noted this some years ago. It may not happen often but with some subjects (super saturated florals for example), Bayer sensor cameras varying resolution across different areas of subject can create a kind of "out of focus in patches" effect.
Unfortunately it actually does not have equal resolution for all the colors. The top layer provides the most exact positional data, while the bottom one the least. The difference grows with large apertures and near the edges of the sensor and ought to manifest itself the most under low SNR conditions.
In addition this is not overly relevant, as in order for there to be significant resolution loss for Bayer for different colored subjects, the color spectrum would have to be of very narrow band. If one simply looks at the raw data, one'll notice that this is almost never the case, but insted most of the time there is quite a bit of data on all the channels which allows for quite nice demosaicing.
Observations from some years ago should be taken with even larger grain of salt than usually, as the demosaicing algorithms improve constantly. Anyhow, I can imagine that the "oof patch" effect is instead the result of pixel peeping area with detail that is too fine to be resolved and is instead blurred by the AA-filter.