On ultrawide (weitwinkel) rectilinear lenses (non-fisheye) the optimum apertures will be f/8-11 or more likely f/11 as beyond this will result in diffraction becoming the limiting factor (due to the small pixel size) and any wider apertures will result in softer corners.
The "diffraction" story is related to the concept of numerical aperture (NA) used for microscopes. The theoretical resolution of the image depends on the solid angle captured by the lens and the wavelength of light. The solid angle basically defines the width of the cone of light emanating from a point that can enter your lens. Larger diameter lenses and wider apertures will thus capture a wider cone. Getting the object closer to the lens also helps a lot. That's why you can stop down macro lenses a lot more without getting into diffraction limitations.
Smaller apertures ALWAYS reduce the resolution of the image projected on the sensor, but most of the time you don't notice because the pixel size of the sensor is the limiting factor (max resolution is about twice the pixel size). Only when the aperture is so small that the resolution becomes lens-limited do you start see degradation of image quality, for many lenses that happens beyond F11 or so. However, for camera with smaller pixels you may hit the limit earlier, or in other words, the smaller pixels can actually extract more resolution from the lens at wider aperture.
The soft corners at wide aperture has nothing to do with resolution and it has everything to do with lens design, quality of the glass and, unfortunately, cost
. That's what James was getting at when he said that top lenses do get a better image, but I think you are right in believing that the distinction gets increasingly less as you close down the aperture. Expensive fast lenses also have the advantage that you can consider teaming them up with a teleconverter of macro-ring while still having enough light left to take decent pictures.
Hope this isn't too confusing. A bit of experience and common sense is worth more than a bucket of theory, but I thought some might like to "dive" a bit deeper into lens physics.
Bart