I own both rifles. I have a custom Shiloh (waited 4 years for it) and a C. Sharps that I bought from existing inventory.
The Shiloh is better in the fit and finish.
Customer Service: Because I purchased both guns from the manufacturer, I dealt with their staff. The staff at Shiloh was always courteous and helpful. My experience with the guy (owner?)at C. Sharps, can't remember his name, was that he was usually a bit touchy and a grouch. I had the impression that once the gun was sold, he didn't want to hear from you.
Hardening of falling block: Both rifles had a characteristic that you may want to keep in mind. The falling blocks on the Shiloh and the C. Sharps were not hardened. As a result some shoters were experiencing a problem where primers that were being blown back against the block face causing a pitting around the area of the firing pin hole. I never experienced this problem with either gun. A fix was developed for it by inserting a case hardened piece of metal where the primer blew back against the falling block.
As I remember it, guns made by Ballard did not have this problem because the blocks were hardened.
I don't know if this problem has been rectified by Shiloh or C. Sharps.
Based on my customer service experience and finish, I'd go with the Shiloh.
The accuracy of the rifles depends very much on your abilities as a handloader to do VERY consistent bullet casting and loading. I use foundry lead, weigh each powder charge and use powder and primers from the same lot, etc. etc. etc. I get good results, particularly with Swiss black powder.
From a competition standpoint, your shooting technique must always be consistent as well. A good spotter who can dope the wind is worth his weight in gold!