With the two merging under the same roof recently, it has become difficult to determine what the major differences between Membase and Couchbase. Why would one be used over the other?
I want to elaborate on the answer given by James.
At the moment Couchbase server is CouchDB with GeoCouch integration out of the box. What is great about CouchDB is that you have the ability to create structured documents and do map-reduce queries on those documents.
Membase server is memcached with persistence and very simple cluster management interface. It's strengths are the ability to do very low latency queries as well as the ability to easily add and remove servers from a cluster.
Late this summer however Membase and CouchDB will be merged together to form the next version of Couchbase. So what will the new version of Couchbase look like?
Right now in Membase the persistence layer for memcached is implemented with SQLite. After the merger of these two products CouchDB will be the new persistence layer. This means that you will get the low latency requests and great cluster management that was provided by Membase and you will also get the great document oriented model that CouchDB is known for.