I'm not sure NoSQL is any more complex than SQL. It all depends on how well the database matches your needs.
In my experience, NoSQL is great if you cannot know your schema beforehand, such as where the user can effectively drive the database schema. It also makes for a good place to store random UI state across user sessions.
SQL is good if you need to slice, dice and mix your data for making fancy charts and any analytics you need to do.
There is no reason why you cannot use both. The application I currently work on uses both. For the part where the user can drive the DB schema or a persistent scratch pad is needed, NoSQL is used. For the reporting and analytic side of the application, SQL is used. The downside is that the application needs two DB engines to work, but with the upside that one doesn't have to force one DB engine to behave like the other.
