Correctly solving a Captcha directly secures the network by contributing to block validation. In order to control the network it will be necessary to have a majority of man-hours, which is impossible in a highly distributed network.
The common alternative, proof-of-stake, ensures existing currency holders control the network and typically receive additional financial benefits. Newcomers to the network are often at a severe disadvantage to the early adopters.
CaptchaCoin's use of proof of human-work balances the playing field: all users are equal independent of the computational power they have or their existing balance. This will ensure a large network that will continually grow with new users who can easily mine their own Caps.
A key feature in their design is scalability. Any given Captcha can be made instantly harder by expanding the range of possible solutions the user has to choose from, meaning the same amount of human-work can be captured using less computing resources.