It all hinges on the flywheel. The big flywheel uses the staggered starter nose cone. The small flywheel uses the in-line holes nose cone.
In the original applications, all 327's use the small flywheel. The 350's are "usualy" the bigger flywheel but there are some smaller flywheel 350's. "Most" big blocks use the larger flywheels but there are just a few very high HP big blocks that do use the smaller flywheel. It does get a bit confusing. You can swap setups if the block is drilled for the other starter nose bolt pattern BUT you need to change the whole enchalada including: the starter nose cone, the 2 bolts, the flywheel, the clutch assy, and the bellhousing. You can not mix and match those parts as they work together as a team.
You could use the smaller disk in the bigger pressure plate but that would be more of a racing type mod where you wanted a little bit of slip to control the launch.