C#

using System;
using System.Text.RegularExpressions;

namespace ThrowAway
{
  public class TMain
  {
    [STAThread]
    public static void Main()
    {
      Regex compiled1 = new Regex( "(a(b)+)+", RegexOptions.Compiled );
      Regex compiled2 = new Regex( "(a(b)+)+", RegexOptions.Compiled );
      Regex noncompiled1 = new Regex( "(a(b)+)+" );
      Regex noncompiled2 = new Regex( "(a(b)+)+" );
      Console.WriteLine( compiled1 == compiled2 );              // Writes False
      Console.WriteLine( compiled1.Equals( compiled2 ) );       // Writes False
      Console.WriteLine( compiled1 == noncompiled1 );           // Writes False
      Console.WriteLine( compiled1.Equals( noncompiled1 ) );    // Writes False
      Console.WriteLine( noncompiled1 == noncompiled2 );        // Writes False
      Console.WriteLine( noncompiled1.Equals( noncompiled2 ) ); // Writes False
    }
  }
}