I've just finished reading the paper. One difference is that Anna offers a weaker form of consistency than etcd. Etcd offers sequential consistency, and Anna offers casual consistency. I believe that this could eliminate many etcd use cases, since ordering for non-casual events many be different depending on the node you access.
I'm not sure I fully understand etcd's durability guarantees. When an operation is completed, does that mean that the data is durable on a single machine, and then becomes durable on other machines at a later point? If so, it seems like Anna could offer the same durability guarantees.
I think Anna's architecture could be more of a competitor to Cassandra, or DynamoDB as long as you only need casual consistency. The performance implications do seem pretty interesting.