I need to create 5 methods on the server side, which will work with binary data. The remote clients are applet and JavaScript. The Client will send files to the server, and
Sounds like your collegue is applying premature optimisation. If you can write it with a JAX-RS library quickly, do so... If it then proves to be the bottleneck only then do you take the time to rewrite as servlet.
In my experience the performance overhead of JAX-RS is not sufficiently big to justify the development and maintenance overhead of writing the equivalent in servlets directly where the problem maps well to JAX-RS