Using string representations of enum values in switch-case

case MyEnum.VALUE1.toString(): // Isn't this equal to "VALUE1" ?

No, not necessarily: you are free to provide your own implementation of toString()

public enum MyType {
VALUE1 {
    public String toString() {
        return "this is my value one";
    }
},

VALUE2 {
    public String toString() {
        return "this is my value two";
    }
}

}

Moreover, someone who is maintaining your code could add this implementation after you leave the company. That is why you should not rely on String values, and stick to using numeric values (as represented by the constants MyEnum.VALUE1, MyEnum.VALUE2, etc.) of your enums instead.