Any other peer to peer solution is partial, and therefore not able to compete with the internet as is. Urbit basically plans around an identity system that prevents spam and abuse; a hierarchical packet routing structure for those identities that doubles as a de facto governance model (due to having a vested interest in the network, the higher up you go); a kernel designed to freeze, and its entire OS on top a series of event logs that mark down computations and new states; a functional language for this "internet where every computer is a database", and the encrypted networking protocol that uses UDP while still ensuring packets always find you.
So if you wanted to, say, have a group of people set as a peer list that others can subscribe to or join, or build or use applications that lets that peer list join chats or see a set of files based upon some arbitrary marker (like giving you $5/mo?) ... you don't need a million services to spread the load, one task per service, each person joining each service. You can just use your own computer. It's a personal server platform for a peer to peer internet. It's an internet designed to resist bad actors, and to resist AOL, to resist Facebook and Google — an internet that facilitates and preserves a Usenet-esque model of small communities doing stuff together on their computers.
(Obvious disclosure that I work on the project, again.)