Main answer: a bigger bucket gives you more photons per unit time. As a bonus, if the seeing conditions support it, the resolution increases with aperture too. See this page for a comparison between a 4" refractor and a C11:
http://www.faintgalaxy.com/ngc6720.htm
However in your case, since you are looking at a big chipped camera you really should be worried about the fully corrected field diameter i.e. the aberration free image circle, or don't bother with a big chip. On a Schmidt-Cass the corrected circle is very small, perhaps <5 mm in diameter, see this pic:
http://www.faintgalaxy.com/ngc6341.htm
the seeing was very good and the increase in coma from the center is evident (magnify the image in your favorite software).
The RC is better than the SC no doubt, but without a field flattener the STL on the RC may still be disappointing, so factor that into the image train. Actually very few telescopes can present a large enough image circle and fully illuminate the STL-11K, and their cost is usually shocking, but they do exist. See here for a comparison:
http://www.faintgalaxy.com/ic0434.htm
same camera as above, close to the same focal length but different optical design.
EB