It's hard to compare because you are missing at least one key number - residual value.
Your cousin isn't buying the car... it appears that he's taking on a lease. Just my opinion - always look beyond what the monthly payment is.
That said, room for negotiation from the private seller will be limited to how much money your cousin can negotiate off of the transfer (less than $6k, or maybe get the private seller to pick up lease transfer fees etc).
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