Spring Rest support is based on MVC and its not actual implementation of JAX-RS.If your application is already on spring and you don’t have any constraint to use Jersey,Spring Rest will make sense.
JAX-RS is just specification and you can replace jersey with apache cxf or RestEasy.
refer : Spring MVC and JAX-RS compliant frameworks
Spring 4 vs Jersey for REST web services
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solved which one is better to implement restful web services among JAX-RS and SPRING RESTFUL API?