When you use glass you have more heat transfer (hot to cold) from the internal environment to the surroundings. Theoretically delta H will be the same whether you do your reaction or experiment in glass or Styrofoam but experimentally you will inevitably record lower temperatures in your glass calorimeter making the calculated value delta H smaller.
This experiment is best done with two Styrofoam cups, one inside the other. I assume you record Ti and Tf. If you allow the glass or cup to equilibrate (10 minutes-room temperature) with your water (example) and then record Ti it should be the same for either instance. When you add your hot metal (example) and record Tf you will transfer (lose) more heat to the surroundings in the glass, therefore you record a lower (incorrect) Tf, which results in a smaller delta T and smaller delta H. The insulation of the Styrofoam reduces this error.