Many of the issues they found with CouchDB have been resolved with Riak. I think the sync API for CouchDB is really cool, but Riak has the auto-sharding thing down cold.
Riak runs map reduce queries across multiple nodes, so performance and capability can grow as you add nodes.
CouchDB's views are neat but they impose some constraints that Riak's more dynamic approach resolves (at the cost of possibly running more queries, but these results can be cached easily giving Riak a form of "views" for often run queries.)
I believe Riak's choices for backend are superior to CouchDB's. Further, Riak supports multiple backends so you can choose the one appropriate for your service (including InnoDB, LevelDB and Basho's Bitcask, as well as a super secret hidden gem of a Caching RAM backend.)
Riak now has indexing of data, and queries on these indexes, but I can't compare it to CouchDB. I can say that the feature is close enough for me to not miss SQL.
I think Riak's "view performance" compared to CouchDB should be good, but may not compare to MySQL, but then, we're talking single node performance. Riak is distributed- you need more performance, you just add nodes and point them at the cluster. MySQL requires you to architect a (from my perspective) brittle configuration of servers that can run into SPF issues.
For instance they talk about having a single write master. What happens when a meteor crashes to earth and takes out that machine? Really unlikely, sure, but I have had enough machines have failures (and failures are often really weird) that I don't trust ANY machine to be a single point of failure. ... and when I'm forced to, like being in a single datacenter or having a single network switch, I don't like it, so I avoid it when I can.
Riak has automatic sharding and automatic rebalancing. It loses a node and keeps running. You add nodes and it redistributes around. Riak is an operational dream.
Not to bash CouchDB at all (or MySQL). I think CouchDB is a great product for certain use cases.
I just think a LOT of people are really missing out by passing over Riak.