I would love to hear a comparison of Dat and Zeronet. The only difference I'm aware of is that Zeronet uses Blockchain technology and the Beaker Browser / Dat folks are of the opinion that Blockchain won't scale for the P2P web.
ZeroNet does not use blockchain tech beyond same cryptography as Bitcoin (and by extension bitcoin addresses). But it does not use "blockchain" for anything core.
You could prob swap this question for "what is the difference between DAT and Bit Torrent" since ZeroNet also uses BT and DAT is similar tech... but this has been answered already.
Outside of this, DAT is agnostic and modular while ZeroNet is focused on p2p website. So a comparison of ZN and Beaker (rather than DAT) would make more sense since both have same focus. Beaker's approach is to use a web browser wrapper (electron/chrome) while ZN is headless and allows you to use your existing web browsers. Beaker is able to offer more/different features because of the tight relationship with a browser app and this affords a powerful path forward beyond just serving static files as web pages. However, ZN also lets you leverage browser database and ability to make simple webapps.
It's really just different approaches to accomplish more or less the same goal of a p2p web. You could say Beaker is more cutting edge because it uses newer DAT (something new) and open to integrating IPFS etc vs being bound to BitTorrent (older tech).
The nice thing is, you can run ZeroNet and Beaker at same time and enjoy both p2p web networks ;-)
From what I can tell (and I am not an expert): Zeronet and IPFS are really fixated with solving the P2P secure content distribution problem. They convolve the solution of that transport-level problem with what I believe to be the central problem, which is a distributed content integrity system. DAT is a technology is that primarily fixated on that latter component, and is relatively independent of transport.
I think that things like p2p transport via Tor, bt, etc. are all red herrings. The robust computing infrastructure for the next-gen, distributed information system that the world needs, should not be tied to transport layer concerns like that. It should work reasonably well via flash-drive-sneakernet as it does over fiber and LTE.
Dat works great in the sneakernet flashdrive scenario as you can P2P sync over offline WiFi and dat clients like beaker browser will automatically verify cryto signatures. It makes distributing a verified offline and online P2P web very accessible for non technical folks. It's like SSL for the offline web.
ZeroNet doesn't use a blockchain. Its only bitcoin related technology is that the site addresses are compatible with bitcoin addresses. You can import the private key into bitcoin and receive funds sent to the address used for the site.