ACID transactions have nothing to do with RDBMS, non relational db's can be and are ACID compliant as well. Look at any object database, you'll generally find MVCC and ACID compliance.

The issue is whether your data fits well into tables and rows, or not, and whether it's worth cramming it into tables and rows and continually reconstructing it to get the benefits relational db's generally provide over the alternatives... which are enforced data integrity, language neutrality, and a generic fixed structure capable of allowing flexible querying. To get those, you trade speed and ease of development.