I don't feel enough experienced with both worlds to properly and fully answer your question, however I'm using a document database for some time and here are some personal hints.
The document databases are based on a concept of key,value, and static views and are pretty cool for finding a set of documents that have a particular value.
They don't conceptualize the relations between documents.
So if your software have to provide advanced "queries" where selection criteria act on several 'types of document' or if you simply need to perform a selection using several elements, the [key,value] concept is not appropriate.
There are also a number of other cases where document databases are inappropriate : presenting large datasets in "paged" tables, sortable on several columns is one of the cases where the performances are low and disk space usage is huge.
So in many cases you'll have to perform "server side" processing in order to pick up the pieces, and with rails, or any other ruby based framework, you might run into performance issues.
The graph database are based on the concept of tripplestore, meaning that they also conceptualize the relations between the entities.
The graph can be traversed using the relations (and entity roles), and might be more convenient when performing searches across relation-structured data.
As I have no experience with graph database, I'm not aware if the graph database can be easily queried/traversed with several criterias, however if an advised reader has such an information I'd really appreciate any examples of such queries/traversals.
I'm currently reading about InfoGrid and trying to figure if such databases could by handy in order to perform complex requests on a very large set of data, relations included ....
From what I can read, the InfoGrah should be considered as a "data federator" able to search/mine the data from several sources (Stores) wich can also be a NoSQL database such as Mongo.
Wich means that you could use a mongo store for updates and InfoGraph for data searching, and maybe spare a lot of cpu and disk when it comes to complex searches inside a nosql database.
Of course it might seem a little "overkill" if your app simply stores a large set of huge binary files in a database and all you need is to perform simple key queries and to retrieve the result. In that cas a nosql database such as mongo or couch would probably be handy.
Hope some of this helps ;)