I've tried NGC which has excellent responsiveness on any guarantee claims, customer service or those who have oversight like Rick Montgomery, Scott Heller have reviewed coins with issues and either taken care of it or described why the coin was properly graded. PCGS on the other hand is a pain, two months of waiting and then usually a denial of the claim of the problem, or a charge by their restoration department and another grading fee. I haven't had experience with claims by Anacs or ICG. Anyone else?
I feel it's important to look at one coin at a time. Both services take care of problems. How many coins have you sent back to PCGS and can you post images?
It's all just going to depend on the coin. They all have guarantees and they all have exceptions. NGC is certainly known for better customer service in most peoples opinion but at the same time they don't back their variety or ancient grading. PCGS does back the varieties for the most part so really you would say that's the stronger one. How any of them work in actual practice has so many variables it is really impossible to say. With that said neither of the big two and probably at least ANACS as well would want to eat a bunch of bad publicity over their mistake and would make mistakes right to preserve their reputation. In my opinion the best guarantee overall is probably CAC.
Actually, PCGS not longer guarantees copper while NGC guarantees it for 10 years. As for customer service, NGC is among the best I have run into while I have heard many complaints about PCGS.
It would be meaningless if NGC *did* guarantee grades on ancients, because nobody grades ancients like that except... NGC. They don't even guarantee authenticity on ancients, and their attributions are frequently wrong. All their slabs are good for when it comes to ancients is increasing the price of the coin.
