Currently the choice between MongoMapper and Mongoid is pretty simple. If you're using Rails 2.3.x, MongoMapper. If you're using Rails 3, Mongoid. The ActiveModel integration is key for Rails 3. Mongoid also has great documentation. MongoMapper does not as much consolidated documentation.
Firstly, MongoModel was started back in November '09 when both MongoModel and and Mongoid were much less mature than they are now. I spent some time contributing patches to MongoMapper but stumbled as I was working on edge rails.
MongoMapper in particular has come a long way since then but still has a few issues in my mind. For example, attributes are converted to/from their mongo representation every single time they are accessed, rather than only when the model is saved or loaded. I also believe MongoModel has a nicer model for typecasting property values (see http://gist.github.com/287379 for an example), and I disagree with the use of has_many associations for embedded collections.
MongoModel isn't perfect either, but it has been the path of least resistance for me in getting my app running on MongoDB.
Cool, thanks for the explanation. Btw, mongoid has a new association dsl that I think makes way more sense. embedded_in, embeds_many, referenced_in, references_many. I bet the project would love to see you as a contributor.
To say 'preferred NoSQL' is far too generic, it is as if users have an option between SQL or NoSQL. I would say that MongoDB is becoming the preferred document-based data store - but that has nothing to do with key value, graph, column-oriented, etc. stores that make up what people refer to as 'NoSQL' (which is a loaded term)
As an admittedly rough measure, check out the number of "watchers" on github for each project's leading plugin:
1106 - MongoMapper http://github.com/jnunemaker/mongomapper
536 - CouchREST http://github.com/jchris/couchrest
312 - Cassandra http://github.com/fauna/cassandra
I've only built one rails app with nosql in it, but at first glance at least Mongo seemed the most fully baked of the group.