Probably more important than adding insulation to an attic itself, is air sealing. Comfenergy air seals the floor of the attic before new TruSoft cellulose insulation is added. This helps to prevent air that you have paid to heat or cool from leaving the home and entering the attic, which is technically "outside" your home. It would be like leaving windows open with the heat running.
If the existing attic insulation is removed and disposed of, then air sealing can be done much better because you can see all of the air leakage locations and nothing is hidden. This picture show one part polyurethane spray foam being used to air seal the attic floor after insulation was removed.