I like Willie's method of cutting and fitting the rectangular tube together, but to add strenght to this joint in bending the addition of either internal or external plates on what is the "web" section of the beam is not very effective. It does strengthen the beam considerabily for side loads but we are usually more concerned with the vertical bending loads and I would think that the best method would be the addition of a diamond shaped doubler plate added to the top of the tube and spanning the weld joint. This increases the moment of inertia thru the joint which makes much stronger. The addition of the side plates also increases the moment of inertia of the section but not nearly as much as a plate on the top. The addition of the lower gusset also does a great job of increasing the moment of inertia of the tube thru the joint and this gusset along with the addition of a diamond shape plate spaning the top weld joint would easily make the tube joint many times stronger than the tube itself.
Rex