What camera/back are you going to use and are you interested in shift/rise fall.
The newer wider Schneiders @28mm, 35mm and 43mm work very well with the digital backs sized from 60mp or smaller. If you get into the 80mp size backs these lenses have issues with the smaller pixel size and can create very challenging shooting conditions, mainly extreme color shifts and loss of details/saturation as you shift off of center. The Rodenstock 23, 28, 32, and 40mm all will work better on the 80mp sized backs. With the 80mp cameras most of the color shifting will not totally correct with a LCC. However on center non-shifted shots the 35mm and 43mm Schneider did very well when I worked with the IQ180 for a few weeks last year
On the other hand the Schneider wides have a less distortion, are much lighter and smaller. The Schneider wides need a Center filter for correcting vignetting (for sure on the 28mm and 35mm) the 43mm is a bit less forgiving. The Rodenstock 23 and 28 and 32 have a physical CF available and I use one on my 28mm, the 40mm does not offer a physical CF and works very well.
I can report that another issue with the Schneiders on 60mp back and 80mp backs is tiling. (Some call it centefolding). This is when you can see faint hard lines showing up on the shot. The lines are from the faint lines that breakup the Phase One sensors (for faster movement of data off the chip). The Schnieders can show these lines in post especially on shifts. The issue may not be a bit one if you are shooting a solid subject, like sky, or water. But the issue can create a problem on certain images and can be hard to fix in post.
Rodenstock wides are designed for optimal performance in the F8 to F11 range but still work very very well towards F5.6 Much past F11 and diffraction will start to creep in. The Schneiders on the other hand seem to prefer the F11 to F16 range, and don't handle the F5.6 to F8 quite as well.
Rodenstock uses a aperture that has no click stops and is smooth, Schneider uses a aperture that has traditional clicks. Electronic shutters are starting to appear for both lenses, but IMO are a bit limited in both range and usage outdoors.
I agree with Marc on the colors in that both brands seems to generate a different look, from my use, the Schneiders are a bit warmer and don't have quite the same contrast that the Rodenstocks have.
For sure any of the wides from either of these companies will out perform the 35mm 45mm, 55mm Mamiya lenses and the newer D glass. Performance against the Phase One LS Schneidrers would most likely be closer. However I still love having tilt control with a wide.