If the shutter and focusing are accurate, the film to lens flange distance correct, and the body internals properly baffled and blackened, you shouldn't see a difference in a Leica body vs. a Bessa body with the same lens. I've had no problems with several Bessa bodies, including the R3A, using both Leica and Cosina-Voigtlander lenses, nor have I heard complaints along these lines on the Cosina Voigtlander Users Group. The image quality with my Leica lenses is the same on the Bessa bodies or the Leica bodies.
The only major difference among bodies that would affect image quality is the baseline of the rangefinder, which varies among both the Leica and Bessa rangefinder bodies. The Leicas in general have longer effective baselines, and so can focus a fast lens at wider apertures and longer focal length lenses more quickly and accurately. With the 1:1 finder, the Bessa R3A isn't bad in that regard. The Bessa T, with the 1.5 magnification rangefinder, is the most accurate of the Bessa focusers. At medium apertures and at shorter focal lengths, the advantage of a longer effective rangefinder baseline diminishes. The Leica cameras themselves have different magnifications (and perhaps some small mechanical baseline differences), so a .85 finder will focus more accurately than a .58. The M3 has a .91 finder magnification. You can find specifics on effective rangefinder baselines for various models on cameraquest.com.
If you check the reviews by Erwin Puts (a Leica lens expert), a number of the C-V lenses rival the Leica lenses proir to current production (i.e. the latest Leica designs) in image quality. The CV 75mm f:2.5 Color Heliar is one of my favorite lenses. Puts says it's a derivative of the rare and highly-regarded Elcan (E.Leitz-Canada) 75mm f:2.5 design, but I didn't know that before I bought, and I trust what I see on the negatives more than anything else.