I think there is a difference in meaning between "He is the nicest person I'm yet to meet" and "I'm yet to meet a nicer person". The first sentence is wrong because you didnt add whom between person and I'm. In my opinion 'He is the nicest person whom I'm yet to meet' is the correct version.
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Anonymous"He is the nicest person I'm yet to meet."It's illogical.
Anonymous"I'm yet to meet a nicer person."This is not idiomatic.