It all depends on process, design and environment in which the contacts are used. Both have excellent conductivity characteristics Both don't oxidize over time On the other hand gold is much softer then carbon, and after hitting that contact a gazillion times there is the potential to displace the gold and allow the underlying Ni to oxidize and prevent contact. As in a situation where the contacts have to be protected by either tape or peelable mask in the assembly process, gold will do better because of its flat and dense surface. Carbon has a rough surface and is more difficult to protect effectively.
Cost evidently will also be a factor in your customer's decision to use carbon. I've used both surfaces in the past and both were equally reliable. When we had problems it was due to design or process related contamination. The failure was never related to the fact it was gold or carbon.
Hope this helps
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