Splitting your application makes sense for the following:
When a certain part of the project needs to have new functionality or bug fixes, you can simply focus on that module and run just the tests for it. Compiling a fraction of all the code and running just the related tests speeds up your work.
You can re-use the code from the modules across different projects. Let's assume your project contains some well-written generic-enough code for mail sending. If you later have another project that need mail sending functionality, you can simply re-use your existing module or build upon it (in another module by adding it as a dependency).
Easier maintainability on the long run. Maybe now it seems like a small project. In a few months things might look different and then you'll need to do more refactoring to split things into logical units (modules).
Conceptual clarity (as added by Adriaan Koster).
Concerning the WAR: You can have an assembly module which puts things together and produces a final WAR file from all the related modules.
Initially, this may seem as more work, but in the long-run, modularized projects are easier to work with and to maintain. Most sane developers would prefer this approach.
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