RootFolder
  Video
    Terminator
    Die Hard
    Rocky
  Music
    Eminem
  Picture
    Picasso
      Do Vinci
      NN
        Cartoon
        Comics
RootFolder1
  Video
    Terminator
    Die Hard
    Rocky
  Music
    Eminem
  Picture
    Picasso
      Do Vinci
      NN
        Cartoon
        Comics
false
true
false

public class TreePrint {

    public static void main(String[] args) {

        Tree<String> rootFolder = new Tree<>("RootFolder");

        Node<String> video = rootFolder.addChild("Video");
        Node<String> music = rootFolder.addChild("Music");
        Node<String> picture = rootFolder.addChild("Picture");

        video.addChild("Terminator");
        video.addChild("Die Hard");
        video.addChild("Rocky");
        music.addChild("Eminem");
        Node<String> picture01 = picture.addChild("Picasso");
        picture01.addChild("Do Vinci");
        Node<String> picture02 = picture01.addChild("NN");
        picture02.addChild("Cartoon");
        picture02.addChild("Comics");
        
         Tree2<String> rootFolder1 = new Tree2<>("RootFolder1");

        Node<String> video1 = rootFolder1.addChild("Video");
        Node<String> music1 = rootFolder1.addChild("Music");
        Node<String> picture1 = rootFolder1.addChild("Picture");

        video1.addChild("Terminator");
        video1.addChild("Die Hard");
        video1.addChild("Rocky");
        music1.addChild("Eminem");
        Node<String> picture001 = picture1.addChild("Picasso");
        picture001.addChild("Do Vinci");
        Node<String> picture002 = picture001.addChild("NN");
        picture002.addChild("Cartoon");
        picture002.addChild("Comics");
        
        
        printTree(rootFolder);
        printTree(rootFolder1);
       
        
        boolean b1 = rootFolder.contains("P0");
        System.out.println(b1);
        boolean b2 = rootFolder1.contains("Eminem");
        System.out.println(b2);
        
        System.out.println(rootFolder.equals(rootFolder1));
      
    }
    
    private static <T> void printTree(Node<T> node) {
        printTree(node, 0);
    }

    private static <T> void printTree(Node<T> node, int level) {
        printNode(node, level);
        if (node.getChildren() != null) {
            for (Node childNode : node.getChildren()) {
                printTree(childNode, level + 1);
            }
        }
    }

    private static <T> void printNode(Node<T> kid, int level) {

        for (int i = 0; i < level; i++) {
            System.out.print("  ");
        }

        System.out.println(kid.getData());
    }
}

-----------------------------------------------------
public class Node<T> {
    private T data;
    private final List<Node<T>> children = new ArrayList<>();
    private final Node<T> parent;

    
    public Node(T data, Node<T> parent) {
        this.data = data;
        this.parent = parent;
    }

    public void addChild(Node<T> node) {
        children.add(node);
    }

   
    public Node<T> addChild(T nodeData) {
    	
    	Node<T> newNode = new Node<T>( nodeData, this ); 
        children.add( newNode );
        return newNode;
    }

   
    public List<Node<T>> iterate() {
        return children;
    }

    public void remove(Node<T> node) {
        children.remove(node);
    }

    public List<Node<T>> getChildren() {
        return children;
    }

    public Node getParent() {
        return parent;
    }

    public T getData() {
        return data;
    }

    public void setData(T data) {
        this.data = data;
    }
    public boolean equals(Object obj) {
    if (this == obj)
        return true;
    if (obj == null)
        return false;
    if (getClass() != obj.getClass())
        return false;
    Node other = (Node) obj;
    if (children == null) {
        if (other.children != null)
            return false;
    } else if (!children.equals(other.children))
        return false;
    if (data == null) {
        if (other.data != null)
            return false;
    } else if (!data.equals(other.data))
        return false;
    return true;
}
}
        

public boolean equals(Object obj) { // этот код сохранился
        return isEquals(obj);
    }
    
    private boolean isEquals(Object obj){  // А этот мне изменить сделать рекурсивным и чтобы правильно работал
        if (this == obj) {
            return true;
        }
        if (obj == null) {
            return false;
        }
        if (getClass() != obj.getClass()) {
            return false;
        }
        Node other = (Node) obj;
        if (children == null) {
            if (other.children != null) {
                return false;
            }
        } else if (!children.equals(other.children)) {
            return false;
        }
        if (data == null) {
            if (other.data != null) {
                return false;
            }
        } else if (!data.equals(other.data)) {
            return false;
        }
        return true;
    }
}