RATIONALE: Drugs used in chemotherapy use different ways to stop cancer cells from dividing so they stop growing or die. Combining chemotherapy with allogeneic or autologous peripheral stem cell transplantation may allow the doctor to give higher doses of chemotherapy drugs and kill more cancer cells.

PURPOSE: Phase II trial to compare the effectiveness of allogeneic stem cell transplantation with that of autologous peripheral stem cell transplantation in treating patients who have non-Hodgkin's lymphoma or Hodgkin's disease.

OBJECTIVES: I. Compare the relapse rate, progression free survival, and overall survival in patients with high risk non-Hodgkin's lymphoma or Hodgkin's disease treated with allogeneic vs autologous stem cell transplantation. II. Compare the toxicities (short and long term) of these 2 regimens in these patients.

OUTLINE: Cytoreductive therapy: Patients receive 3 courses of salvage chemotherapy (e.g., dexamethasone, high dose cytarabine, and cisplatin (DHAP); etoposide, methylprednisolone, high dose cytarabine, and cisplatin (ESHAP); fludarabine, mitoxantrone, and dexamethasone (FND)). Harvest: Patients with an HLA identical sibling donor are assigned to the allogeneic peripheral blood stem cell (PBSC) transplantation group. Patients without an HLA identical sibling are assigned to the autologous PBSC transplantation group. Allogeneic OR autologous PBSC are harvested. Conditioning regimen: Patients receive high dose chemotherapy comprised of cyclophosphamide IV over 1 hour on days -6 to -3 and carmustine IV over 3 hours and etoposide IV over 3 hours on days -6 to -4. PBSC are infused on day 0. Patients are followed weekly for 3 months, then monthly for 1 year, and then annually thereafter.

PROJECTED ACCRUAL: A total of 120 patients will be accrued for this study over 4 years.

DISEASE CHARACTERISTICS: Histologically proven non-Hodgkin's lymphoma that has relapsed or failed to achieve complete remission after first line induction chemotherapy Intermediate or high grade (including mantle cell, but excluding lymphoblastic disease) No more than 1 prior salvage chemotherapy regimen, e.g.: Dexamethasone, high dose cytarabine, and cisplatin (DHAP) Etoposide, methylprednisolone, high dose cytarabine, and cisplatin (ESHAP) Low grade No more than 2 prior salvage chemotherapy regimens, e.g.: Fludarabine, mitoxantrone, and dexamethasone (FND) ESHAP DHAP OR Histologically proven stage III or IV Hodgkin's disease that has relapsed or failed to achieve remission after combination induction chemotherapy Prior primary radiotherapy allowed if relapse is high risk (e.g., recurrence in radiation field, B symptoms, liver/marrow involvement) No more than 2 prior salvage chemotherapy regimens Allogeneic stem cell transplantation group: Availability of 6 antigen (A, B, and DR loci) HLA matched sibling donor No active CNS disease A new classification scheme for adult non-Hodgkin's lymphoma has been adopted by PDQ. The terminology of "indolent" or "aggressive" lymphoma will replace the former terminology of "low", "intermediate", or "high" grade lymphoma. However, this protocol uses the former terminology.

PATIENT CHARACTERISTICS: Age: 15 to 55 Performance status: ECOG 0 or 1 Life expectancy: Not specified Hematopoietic: Not specified Hepatic: Bilirubin no greater than 2.0 mg/dL SGOT and SGPT no greater than 3 times normal PT and PTT normal Renal: Creatinine no greater than 2.0 mg/dL Creatinine clearance at least 60 mL/min Cardiovascular: LVEF at least 45% by MUGA scan or echocardiogram No myocardial infarction within the past 6 months No arrhythmias unless medically controlled Pulmonary: FEV1 at least 50% predicted DLCO at least 50% predicted Other: No diabetes mellitus or thyroid disease unless medically controlled No active serious infection HIV negative Not pregnant or nursing Negative pregnancy test

PRIOR CONCURRENT THERAPY: See Disease Characteristics