Over the past decade I've realised using a RDBMS is the right call basically 100% of the time. Now pgsql has jsonb column types that work great, I cannot see why you would ever use a NoSQL DB, unless you are working at such crazy scale postgres wouldn't work. In 99.999% of cases people are not.
In retrospect we should have gone with mongo from the start, but postgres was chosen because in 99% of circumstances it is good enough. It was the wrong decision for the right reasons.
So really the use case for mongo etc is 'very high performance requirements' AND 'does not require relations'.
Many projects may be ok with just one of those. But very few require meet both of those constraints.
FWIW I've seen many cases which are sort of the opposite: great performance with mongodb, but then because of the lack of relations for a reporting feature (for example) performance completely plummets due to horrible hacks being done to query the data model that doesn't work with the schema, eventually requiring a rewrite to RDBMS. I would guess that this is much more common.
If your company needs to shutdown RDS to save a couple of bucks a month, there's a much larger problem at hand than RDS vs Dynamo.
As far as what makes Dynamo a good fit, I almost take the other approach and try to ask myself, what makes Postgres a bad fit? Postgres is so flexible and powerful that IMO you need a really good reason to walk away from that as the default.