If you ask Alfresco they would probably say "REST API" because they've been putting a lot of engineering effort into improving it lately so it will work better with client-side frameworks such as their own Alfresco Developer Framework (ADF).
But the decision should be more about what exactly it is that you need to do and how easy it is for you to work with either of the APIs using your skills and preferred toolets and frameworks. From the high level requirements you've given, either one will work, but I suspect once you dive into the details and line those up against the capabilities of each API, you will start to develop your own preference.
The biggest driver is how closely coupled do you want to be to the Alfresco repository. If you go with the Alfresco REST API and then later decide to use a different repository, everywhere you've made a call to the repo will have to be refactored. If you go with CMIS, there will still likely be some refactoring but it could be less.
