Basic difference between the two is the Synchronization. Vector is Synchronized and Arraylist is not. If your application will  be having single thread of execution use Arraylist else Vector.

ArrayList is fast because its not synchronized. Its not a legacy class and was introduced in JDK 1.2. It uses Iterator interface to traverse the elements and once element exceeds the capacity it increment the size by 50% of current array size.

Vector is slow due to synchronization. Its legacy class and use both Enumeration and Iterator to traverse the elements. And once the element exceed the capacity it increment the size by 100% of current size.

Both implements the List interface and maintains the insertion order.

Following is sample ArrayList Code:

      ArrayList arrayList= new ArrayList();
      // Add elements to the array list
      arrayList.add("CC");
      arrayList.add("AA");
      arrayList.add("DD");
      // Adding element at second position i.e. after CC
      al.add(1, "A2");

      // al.size() inform number of elements in ArrayList
      System.out.println("ArrayListSize :"+al.size());

      // Removing AA record from the ArrayList
      al.remove("AA");
      // Removing element at third position i.e. DD
      al.remove(2);

      // Get elements of ArrayList
      for(int i=0;i<al.size();i++)
      {
         System.out.println("ArrayList Element "+i+" :"+al.get(i));
      }

Following is the sample Vector Code:

        Vector<String> vect=new Vector<String>();

        // Add elements to vector 
        vect.add("CC");
        vect.add("AA");
        vect.add("DD");
        
        // Add vector element at after CC
        vect.add(1, "A2");
 
        // vect.size() inform number of elements in Vector
        System.out.println("Vector Size :"+vect.size());

        // Removing AA record from the ArrayList
        vect.remove("AA");
        // Removing element at third position i.e. DD
        vect.remove(2);

        // Get elements of Vector 
        for(int i=0;i<vect.size();i++)
        {
            System.out.println("Vector Element "+i+" :"+vect.get(i));
        }