I loved the premise of Unite; it was a home HTTP server with dynamic DNS via an opera-run service. Very cool idea, but it wasn't that good of a product experience. (Maybe somebody should try it again using Electron; "node in your browser" isn't that bad of a pitch.)
But, one of the big problems with a bunch of home HTTP servers is availability. The crypto-p2p network lets you push to a public peer and solve availability and improve transfer speed, without having to change the URL. That's a pretty big deal when you consider how unreliable the edge network is.
The other really key difference is that P2P removes the service dependency; sites/apps sync to your device, and then use device APIs to get work done. It's a different view of the applications model, and it means recipients can modify the application after download. This is a really big part of our focus; all sites and apps are user-modifiable.
Zeronet made decisions with their technology stack that I disagreed with, but it's in spirit very near to us, and I've always loved the polish of their applications and demos. P2P is pretty competitive right now. Some projects involve blockchains, some involve BitTorrent, some involve IPFS. We use Dat, and there are technical reasons behind why we chose Dat, but in the end this space will differentiate by the end-user experience.