Comparing Two Different Myeloablation Therapies in Treating Young Patients Who Are Undergoing a Stem Cell Transplant for High-Risk Neuroblastoma

Inclusion Criteria:

* Diagnosis of neuroblastoma or ganglioneuroblastoma by histology or as evidenced by the presence of clumps of tumor cells in bone marrow and elevated catecholamine metabolites in urine meeting any of the following criteria:

  * Patients with newly diagnosed neuroblastoma with International Neuroblastoma Staging System (INSS) stage 4 disease are eligible with the following:

    * MYCN amplification (i.e., greater than four-fold increase in MYCN signals as compared to reference signals), regardless of age or additional biologic features
    * Age \> 18 months (i.e., \> 547 days) regardless of biologic features
    * Age 12-18 months (i.e., 365-547 days) with none of the following three favorable biologic features (i.e., non-amplified MYCN, favorable pathology, and deoxyribonucleic acid \[DNA\] index \> 1)
  * Patients with newly diagnosed neuroblastoma with INSS stage 3 are eligible with the following:

    * MYCN amplification (i.e., greater than four-fold increase in MYCN signals as compared to reference signals), regardless of age or additional biologic features
    * Age \> 18 months (i.e., \> 547 days) with unfavorable pathology, regardless of MYCN status
  * Patients with newly diagnosed INSS stage 2a or 2b with MYCN amplification (i.e., greater than four-fold increase in MYCN signals as compared to reference signals), regardless of age or additional biologic features
  * Patients with newly diagnosed INSS stage 4s with MYCN amplification (i.e., greater than four-fold increase in MYCN signals as compared to reference signals), regardless of additional biologic features
  * Patients \>= 365 days initially diagnosed with INSS stage 1, 2, or 4S and who progressed to a stage 4 without interval chemotherapy

    * Must have been enrolled on COG-ANBL00B1
* Creatinine clearance or radioisotope glomerular filtration rate ? 70mL/min OR serum creatinine based on age/gender as follows:

  * 1 month to \< 6 months: 0.4 mg/dL
  * 6 months to \< 1 year: 0.5 mg/dL
  * 1 to \< 2 years: 0.6 mg/dL
  * 2 to \< 6 years: 0.8 mg/dL
  * 6 to \< 10 years: 1 mg/dL
  * 10 to \< 13 years: 1.2 mg/dL
  * 10 to \< 16 years: 1.5 mg/dL (male), 1.4 mg/dL (female)
  * \>= 16 years: 1.7 mg/dL (male), 1.4 mg/dL (female)
* Total bilirubin ? 1.5 times upper limit of normal (ULN) for age
* Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) \< 10 times ULN for age
* Not pregnant or nursing
* Negative pregnancy test
* Shortening fraction \>= 27% by echocardiogram (ECHO) OR left ventricular ejection fraction (LVEF) \>= 50% by radionuclide angiogram
* No known contraindication (e.g., size, weight or physical condition) to peripheral blood stem cell collection
* No prior systemic therapy except for localized emergency radiation to sites of life-threatening or function-threatening disease
* No more than one course of chemotherapy per low- or intermediate-risk neuroblastoma therapy prior to determination of MYCN amplification and histology