Spring HandlerInterceptor vs Servlet Filters
The org.springframework.web.servlet.HanderInterceptor
Interface JavaDoc itself has a two paragraphs that discuss this question:
HandlerInterceptor is basically similar to a Servlet 2.3 Filter, but in contrast to the latter it just allows custom pre-processing with the option of prohibiting the execution of the handler itself, and custom post-processing. Filters are more powerful, for example they allow for exchanging the request and response objects that are handed down the chain. Note that a filter gets configured in web.xml, a HandlerInterceptor in the application context.
As a basic guideline, fine-grained handler-related preprocessing tasks are candidates for HandlerInterceptor implementations, especially factored-out common handler code and authorization checks. On the other hand, a Filter is well-suited for request content and view content handling, like multipart forms and GZIP compression. This typically shows when one needs to map the filter to certain content types (e.g. images), or to all requests.
Spring Handler interceptors allow you to hook into more parts of the request lifecycle, and get access to more information in the process. They're often more intimately coupled to the request/response cycle than filters.
Filters are more suitable when treating your request/response as a black box system. They'll work regardless of how the servlet is implemented.
If you're using Spring MVC, there's little reason to write new logic as a servlet filter. Everything filters can do, interceptors can do more easily and more elegantly.
Remember also, servlet filters have been around for much longer than interceptors.