Pros: It makes attacks using commodity hardware (eg, botnets, which are one of the more serious threats at the moment) much less efficient, which increases security. By the same token, it provides the same level of security against such attacks while consuming far less energy (the amount of energy used in bitcoin mining is something detractors are constantly complaining about for some reason).

Cons: No prototype has ever been publicly demonstrated, and they may not actually exist yet, despite claims to the contrary. Some have accused the manufacturers of being scammers, though it's entirely possible their suspicious behaviour is a desperate attempt to avoid the fate of the Osborne Computer Corporation (whose premature announcement of a relatively advanced, but not-yet-existent computer system led directly to the company's bankruptcy when customers cancelled their orders for existing products and as a result the company didn't have enough money coming in to actually develop and release the new system).