scala> classOf[String] match { case x if x == classOf[String] => "matched" }
res1: java.lang.String = matched

scala> val StringClass = classOf[String]
StringClass: java.lang.Class[String] = class java.lang.String

scala> classOf[String] match { case StringClass => "matched" }
res2: java.lang.String = matched

scala> val stringClass = classOf[String]
stringClass: java.lang.Class[String] = class java.lang.String

scala> classOf[String] match { case `stringClass` => "matched" }
res3: java.lang.String = matched