P2P exchanges offer high resistance to transaction censorship, are cheap to use, private and secure; at least when realized properly. All advantages of decentralized cryptocurrency exchanges arise from not having a single company in charge of things. A single point of authority offers some advantages - primarily, the faster trades. However, it also works as the single point of failure, meaning that every bit of damage to it affects the entire system. So here are the advantages of the P2P exchanges, achieved by removing that single point of failure.
Transaction censorship resistance.
Regular cryptocurrency exchanges are run by people - they are vulnerable, and may be exploited by governments by imposing regulatory restrictions. Case in point: the recent intervention by the People’s Bank of China, which lead to two of the largest exchanges in China freezing all Bitcoin withdrawals for a month. As a user, you wouldn’t want that to happen to your funds.
On the other hand, P2P exchanges are practically invulnerable to government interference, because they don’t have any central point of authority which could be coerced. Even if some parts are forced to cease their operations, the rest of the system remains unaffected. This advantage is exactly what has caused a sharp increase in the user base of LocalBitcoins, one of the top P2P exchanges, following the aforementioned PBoC’s actions.
Cheap operations. Again, regular exchanges are operated by people, who have to be paid for their work. P2P exchanges are run by software, so there’s little to no corporate overhead, and, by extension, very small fees for the users, if any. Privacy. Over the recent years, governments around the globe have been successfully enforcing AML and KYC regulations on cryptocurrency exchanges. This oversight forces the companies running those exchanges to collect as much info on their users as possible: names, places of residence, ID numbers and more.
It goes without saying that government cannot impose those regulations on P2P exchanges, which means that trades can be conducted in a much more private manner there. Security. P2P exchanges do not hold Bitcoins for their users - instead, they connect traders, allowing them to conduct deals directly. Not having to entrust your coins to a third party makes the process much safer. If nobody holds your funds but you, then nobody can steal or lose them - intentionally, or accidentally.