同じクラス名は避けるべし

重大: Mapping conflict. A Servlet registration exists with same mapping as the Jersey servlet application, named jp.unko.hoge1.resources.MyApplication, at the servlet mapping, /rest/*. The Jersey servlet is not deployed.
重大: Mapping conflict. A Servlet registration exists with same mapping as the Jersey servlet application, named jp.unko.hoge2.resources.MyApplication, at the servlet mapping, /rest/*. The Jersey servlet is not deployed.

hoge1アプリケーションからhoge2の.jarに依存を張っていて、その両方に同じクラス名のクラスがあるとまずいっぽい。
あ クラス名ってより@Pathか