As a rule of thumb: For Scala, use Play. For Java, use Jersey.
You can use Jersey/Scala and Play/Java; I've done both. It works. It isn't bad. But unless you have a particular reason to do that, I wouldn't mix ecosystems. Java and Scala are interoperable but they have different ecosystems, I would avoid adding Java-isms if you are using Scala or Scala-isms and dependencies if you are running straight Java.
Jersey and Play are generally close for REST services. Neither really has any killer features over the other.
Jersey defines URL mappings in annotations, Play defines them in a service wide route file. And they bundle or have varying quality of integration with different libraries for things like XML, JSON, database, testing, mocking, dependency injection libraries and app server deployment.
The Java world has JMS, Spring, JUnit, jdbi/hibernate/jpa, Jetty/Grizzly. The Scala world has Akka, specs2/ScalaTest, Anorm/slick. Jersey is a better fit for the first world, Scala for the second. You can definitely cross that, but it will be a little less elegant and might require more glue coding.