Some further reading : https://netsec.ethz.ch/publications/papers/ariadne.pdf
it's generally seen as more secure and in cases more efficient.
> Ariadne enhances previous approaches to preserve communication privacy by introducing two novelties. First, the source route is encoded in a fixed size, sequentially encrypted vector of routing information elements, in which the elements' positions in the vector are pseudo-randomly permuted. Second, the temporary keys used to process the packets on the path are referenced using mutually known encrypted patterns. This avoids the use of an explicit key reference that could be used to de-anonymize the communications.
> Ariadne is efficient, using only highly efficient symmetric cryptographic primitives.
Your implementation is up to you really. As I see the OP's link, this is just an aperiodic implementation of the Ariadne protocol in Rust ?
To your original question on the benefits over a standard AEAD:
For stateless encryption, our `ariadne-etm` crate offers no major advantage. The core protocol, however, is a programmable, stateful cryptographic engine. This enables new protocol designs.
For example:
1. Smarter Transport Layers. The Labyrinth can be a public parameter derived from a server's key. This allows building in features like proof-of-work for DoS resistance or cryptographic watermarks for traitor-tracing directly into the transport layer.
2. Verifiable Stateful Computation. The architecture allows proving that a secret, stateful program was honestly executed over a verifiable duration. The program's execution path leaves an irreversible "scar" on a one-time-use Labyrinth, creating a commitment to the entire computational history.
The point isn't to replace AES. It's a new foundation for different kinds of cryptographic systems.