I'd like to add couple of things to Bryan's answer.
Limitations of each DB in comparison to other:
If you notice the pattern above you'd figure that
In MongoDB: Keep your frequent reads. Dump the unknown. Store the nested data for which the nested content's scope is isolated to its root parent (mongo document) but not outside. Keep the computed snapshots.
In MySQL: Anything that's Relational across entities. Anything that is Transactional goes here, you cannot mess with it without rollbacks.
Having said that above, both DBs are capable of handling their limitations with some workarounds although those are not recommended.