I don't think the question should be unstructured vs. unstructured data. It's more about performance for large quantities of data. I have some experience trying to make a SQL database into a non-structured data store. In my case, I had a bunch of dynamic (JSON) objects that needed to go into a table. I was using SQL because the objects were related to one another through parent-child relationships (i.e. a self-join). It worked fine for a test data set of about 5,000 objects.
Using SQL
HOWEVER, my production database contains about 3gb worth of data (about 1 million objects, give or take). I spent weeks building and optimizing my sql joins and queries. I was able to achieve a maximum performance of about 10ms to return a few nodes from a selected spot in the tree. Then, I ran into strange query performance issues that could only be solved by re-structuring the indices and/or dropping and re-creating the stored procedures. I was spending as much time maintaining the damn SQL database as I was coding the rest of my application. Not good. (Oh, and I should mention that I have about 3 years of hands-on DBA experience with SQL server, so I am by no means new to the game).
Using Couchbase
Fast-forward 18 months. I am now using Couchbase
(a popular nosql database). I was able to get the identical functionality from CB by using views and map/reduce. I spent one week getting my CB deployment up and running. Latency on query lookups is sub-millisecond. The end user notices a dramatic increase in performance.
Bottom Line
If you have a lot of data, you are going to be hard-pressed to find a situation where SQL will come anywhere near the performance of a nosql database architecture, regardless of how structured or unstructured the data is.