Low-Dose or High-Dose Conditioning Followed by Peripheral Blood Stem Cell Transplant in Treating Patients With Myelodysplastic Syndrome or Acute Myelogenous Leukemia

Inclusion Criteria: * Myelodysplastic syndrome (MDS) or transformed acute myelogenous leukemia (transformed from MDS) * De novo acute myelogenous leukemia (AML) beyond first remission * Intermediate or high risk de novo AML in first complete response (at FHCRC unrelated donor recipients only) * Chemotherapy required prior to HCT for all patients: * A) Interval between start of a cycle of cytoreductive chemotherapy and infusion of donor stem cells must be at least 30 days; chemotherapy received for disease maintenance will be allowed during this time period * B) All patients must have \< 5% myeloblasts based on marrow morphology performed within 21 days prior to start of conditioning regimen and at least 3-4 weeks after the start of pre-transplant cytoreductive chemotherapy * C) All patients must have no circulating peripheral blood myeloblasts present based on morphologic analysis * Age 65 years or under for patients with related donors; age 60 years or under for patients with unrelated donors * HCT-Specific Comorbidity Index Score (HCT-CI) \< 3 * Related donor (age \> 12 years, nonsyngeneic) or unrelated donor, HLA phenotypically or genotypically identical at the allele level at A,B,C,DRQ1, and CBQ1 * DONOR: Related or unrelated donors who are genotypically or phenotypically matched by high resolution HLA typing (HLA-A, B, C, DRB1, and DQB1); class 1 single allele mismatch allowed * DONOR: Patient and donor pairs homozygous at a mismatched allele in the graft rejection vector are considered a two-allele mismatch, i.e., the patient is A\*0101 and the donor is A\*0201, and this type of mismatch is not allowed * DONOR: A positive anti-donor cytotoxic crossmatch or flow cytometric assay is an absolute donor exclusion at FHCRC/SCCA * DONOR: Age \>= 12 years * DONOR: Donors must consent to PBSC mobilization with G-CSF and leukaphereses; bone marrow as a source of stem cells will not be allowed * DONOR: Donor must have adequate veins for leukaphereses or agree to placement of central venous catheter (femoral, subclavian) Exclusion Criteria: * HIV seropositivity * Fungal infections with radiographic progression after appropriate therapy for greater than one month * Organ dysfunction * Symptomatic coronary artery disease or ejection fraction \< 35% * DLCO \< 65%, FEV1 \< 65% or receiving supplementary continuous oxygen * Liver function abnormalities: Patients with clinical or laboratory evidence of liver disease will be evaluated for the cause of liver disease, its clinical severity in terms of liver function, histology, and the degree of portal hypertension; patients with fulminant liver failure, cirrhosis with evidence of portal hypertension or bridging fibrosis, alcoholic hepatitis, esophageal varices, a history of bleeding esophageal varices, hepatic encephalopathy, uncorrectable hepatic synthetic dysfunction evidenced by prolongation of the prothrombin time, ascites related to portal hypertension, bacterial or fungal liver abscess, biliary obstruction, chronic viral hepatitis with total serum bilirubin \> 3 mg/dL, and symptomatic biliary disease will be excluded * Karnofsky Performance Score \< 70 * Lansky-Play Performance Score \< 70 for pediatric patients * Life expectancy severely limited (\< 2 years) by disease other than MDS/AML * Fertile men and women unwilling to use contraceptive techniques during and for 12 months following treatment * Patients with active non-hematological malignancies except: * A) Patients with follicular or low grade lymphoma will be eligible as long as they have not and do not require active treatment for control of their disease * B) Patients with localized non-melanoma skin malignancies * Patients with poorly controlled hypertension who are unable to have blood pressure stabilized below 150/90 mm Hg on standard medication * Females who are pregnant or breastfeeding * Patients with systemic, uncontrolled infections * Active CNS disease as identified by positive CSF cytospin * DONOR: Identical twin * DONOR: Age \< 12 years * DONOR: Pregnancy * DONOR: HIV seropositivity * DONOR: Inability to achieve adequate venous access * DONOR: Known adverse reaction to G-CSF