For example: Microsoft SQL Server vs. CouchDB.
The main benefit for me with CouchDB is that you can access it from pretty much anywhere! What advantages does a document based database have over a relational one?
Where would a document based db be a better choice over a relational?
I wouldn't say "accessing it from anywhere" is an advantage of CouchDB over SQL Server. Both are fully accessible from a variety of clients.
The key differentiating factor is the fundamental concept of how data is persisted as tables & columns (SQL Server) versus documents (CouchDB). In addition, CouchDB is designed to leverage multiple copies with replication/map-reduce in a highly forgiving fashion. SQL Server can do the same level of fault tolerance but true map-reduce is non-existant in it (it's ability to deal with sets mimics the capabilities fundamentally however - see GROUPING SETS keyword).
You should note this post which really shows that map reduce has its place, but you need to pick the right tool for the job:
http://gigaom.com/2009/04/14/mapreduce-vs-sql-its-not-one-or-the-other/