Maven advantages over ant are quite a few. I try to summarize them here.
Convention over Configuration
Maven uses a distinctive approach for the project layout and startup, that makes easy to just jump in a project. Usually it only takes the checkount and the maven command to get the artifacts of the project.
Project Modularization
Project conventions suggest (or better, force) the developer to modularize the project. Instead of a monolithic project you are often forced to divide your project in smaller sub components, which make it easier debug and manage the overall project structure
Dependency Management and Project Lifecycle
Overall, with a good SCM configuration and an internal repository, the dependency management is quite easy, and you are again forced to think in terms of Project Lifecycle - component versions, release management and so on. A little more complex than the ant something, but again, an improvement in quality of the project.
What is wrong with maven?
Maven is not easy. The build cycle (what gets done and when) is not so clear within the POM. Also, some issue arise with the quality of components and missing dependencies in public repositories.
The best approach (to me) is to have an internal repository for caching (and keeping) dependencies around, and to apply to release management of components. For projects bigger than the sample projects in a book, you will thank maven before or after
