The C6 is physically larger in all dimensions the fit into the transmission tunnel will be tight. It's heavier. Being longer, it won't quite mate up to the C4's crossmember. The C6's cooling lines are in a different positition. The C6 has to be mated to a "C6" flexplate (something about offset or depth, I forget). The shift linkage is different, not terribly so, but diiferent.
The kicker is the tailshaft has a different spline count, your C4 driveshaft's front yoke will NOT work. Also since the C6 is longer, I believe you will need a slightly shorter driveshaft.
An AOD at least can use the C4's yoke, as the tailshaft splines are the same. Hint, hint.