First, like I'm sure a lot of people will mention, Ant and Maven are not exactly intended to solve the same goals. Since you said you understand what each provides, I won't get into the details of that, so suffice it to say that Ant lets you define the details of how to build individual components, while Maven manages the dependencies between components plus Maven lets you define a complete project build cycle from compile through test and deploy in a programmatic way.
I've used Maven on a couple projects in the past, and I just started using it on another one recently. There are plenty of articles on the net that compare Ant and Maven, so you can look at those, but from my experience, its always worthwhile to consider how you can improve a project. Dependency management and build lifecycle are two important aspects of any large project, and Maven helps in both those areas. If you already have a good build system in place using ant, and your dependencies are kept in a easy to access central location, and you don't plan on extending your build process to include any more advanced build management, then maybe you should stay with what you have.
On the other hand, if you want to use a continuous integration server like hudson or an artifact repository like nexus, then moving your project to maven can really help with build efficiency and automation. You probably would like maven in those situations because the full cycle from dependency to build to artifact can be achieved using those types of tools and you'll be able to better control your builds and releases. On my current project we have many modules and dependencies, like you mention. Migrating to maven so we could use hudson and nexus really helped because we could drop all those 3rd party jars into a nexus repository and stop having to check them into version control or email them around. Also, builds were out of hand because the CM people had a build plan as a document that they would sometimes follow, but making that part of your project (i.e., the pom.xml) defines how you are supposed to build and lets you enforce it. Maven is the glue that holds all of those things together.
In the end, its a matter of how long you expect the project to last, how good your process is now, whether you want to clean up your dependencies, whether you want to enforce your build plan, and whether you want to have the option to use continuous integration and artifact management. If you any of those things, Maven is a strong candidate.