This randomized phase III trial is studying low-dose prednisone or methylprednisolone to see how well they work compared with standard-dose prednisone or methylprednisolone in treating patients with newly diagnosed acute graft-versus-host disease (GVHD). Glucocorticoids, such as prednisone or methylprednisolone at a starting dose of 2 mg/kg/day are standard treatment for acute graft-versus-host disease caused by a donor stem cell transplant. It is not yet known whether low-dose glucocorticoids are more effective than standard-dose glucocorticoids in treating acute graft-versus-host-disease