The JavaScript API builds on, i.e. utilizes, the REST API. In fact, all ESRI clients provide language/environment specific bindings (e.g. SilverLight, Flex, WPF, JavaScript, iOS, Andriod, etc.) which use the REST API.
If you are developing in JavaScript then you should strongly consider using the JavaScript API otherwise you have a lot of plumbing to do.
Why would you not use one of the ESRI APIs?
- You are running in an environment for which no API is available, e.g. an IBM mainframe.
- The licensing terms and conditions of using the APIs are, for whatever reason, unacceptable to you.