There are some use cases where adopting RDS might prove an antipattern.

In case of key/value data structure or data structure is unpredictable, or not yet well defined, and when automated scalability is a requirement --> DynamoDB is more suitable.

In case of large binary objects --> S3 could be a better choice.

In case of other database platforms like IBM DB2 or SAP HANA, or if you need root access, then an EC2 would be the solution. Since RDS is a managed service you don't have root access to OS and therefore you can't install software such as management tools, if that is your requirement EC2 will give you a greater level of control over your DB and the underlying server OS, but you will have to manage everything yourself ( backups, redundancy, scaling - and basically all the administrative tasks we have seen above).