What are the advantages of chain-of-responsibility vs. lists of classes?

I like your idea with collection better than those successors. It makes it easy and clear to manipulate this set of handlers: the collections interface is well known and everybody understands how to iterate over a List or what not.

If you use this successor way suggested by a friend, take care not to fall into a very deep recursion (unless your platform supports tail calls, I don't know if JVMs are capable of that).

I wouldn't recommend adding any methods to the collection. You get much more complicated design that's harder to comprehend and harder to modify. There are two separate concerns: storing a set of handlers and the interpretation of this handlers as a chain of responsibility. A method that handles requests by iterating over a collection is on higher level of abstraction than collection housekeeping methods, therefore shouldn't belong to collection interface.

Which approach is best depends on what your handlers want to do.

If the handlers can completely handle a request request on their own, your approach is fine. The handlers do not have a reference to other handlers, which makes the handler interface simple. Unlike the standard implementation of Chain of Responsibility, you can add or remove handlers from the middle of the chain. In fact, you can choose to build different chains depending on the type of request.

One problem with your approach is that a handler cannot do pre-processing or post-processing on the request. If this functionality is required, then Chain of Responsibility is better. In CoR, the handler is the one responsible for delegating to the next handler on the chain, so the handler can do pre-processing and/or post-processing, including modifying or replacing the response from the next handler on the chain. In this way, CoR is very similar to Decorator; it's just the intent that's different.

Since in CoR, the handler keeps a reference to the next item on the chain, you cannot add or remove items from the middle of the chain. A variation of CoR that allows you to add or remove items from the middle of the chain is a Filter Chain (see, for example, javax.servlet.FilterChain).

The code example you showed was a bunch of "if" statements that did different behavior based on the type of an object. If that is typical for the code you are cleaning up, you can simply have a map from the request type to the handler required.

Another approach to removing "if" statements is inheritance. If you had some behavior that you needed to do, and there was one variation for a web server, and other variation for a SOAP server, you could have a WebServerRequestHandler and a SoapServerRequestHandler, each extending RequestHandler. The advantage with inheritance is there a clearer place to put logic that is common to both types of request. The disadvantage is that since Java doesn't have multiple inheritance, you can only model single-dimensional problems.