Cisplatin and Fluorouracil Compared With Carboplatin and Paclitaxel in Treating Patients With Inoperable Locally Recurrent or Metastatic Anal Cancer

Inclusion Criteria: * Inoperable, locally recurrent or metastatic disease (tumor resectability should be assessed by a local surgeon or multidisciplinary team) * Histological or cytological confirmation of epidermoid anal carcinoma (includes squamous, basaloid and cloacogenic lesions) from the primary tumor or a newly diagnosed recurrent/metastatic lesion * Eastern Cooperative Oncology Group (ECOG) performance status (PS) =\< 2 * Measurable disease according to Response Evaluation Criteria in Solid Tumors (RECIST) criteria version 1.1 * Previous definitive chemo-radiation is permitted for early stage tumors (cisplatin-based chemotherapy \[chemo\]-radiation is permitted but only if tumor progression/relapse occurs after 6 months from treatment completion) * Previous systemic chemotherapy is permitted if administered as induction treatment (=\< 2 cycles) before definitive chemoradiotherapy for early stage disease and there is no evidence of tumor progression during or after treatment completion * Human immunodeficiency virus positive (HIV+) patients will be considered eligible if they are on highly active anti-retroviral therapy (HAART) and have a cluster of differentiation (CD)4 count of \>= 200/ul (HIV+ patients who are on HAART and have a CD4 count \< 200/ul are eligible if the plasma viral load is below the level of detection according to the local assay) * Absolute neutrophil count (ANC) \>= 1.5 x 10\^9/l * Platelets \>= 100 x 10\^9/l * Hemoglobin (Hb) \>= 9 g/dl for males and \>= 8 g/dl for females * Creatinine clearance \>= 50 ml/minute * Serum bilirubin =\< 1.5 x upper limit of normal (ULN) * Alanine transaminase (ALT) or aspartate transaminase (AST) =\< 3 x ULN (if liver metastases are present, serum transaminases =\< 5 x ULN are permitted) * Fertile men and women must agree to take adequate contraceptive precautions during, and for at least six months after therapy * Life expectancy of at least 3 months Exclusion Criteria: * Tumors of adenocarcinoma, melanoma, small cell and basal cell histology are excluded * Locally recurrent tumor which is amenable to curative resection (as deemed by a local surgeon or multidisciplinary team) * Tumor relapse/progression within 6 months of completion of a cisplatin-based chemoradiotherapy regimen for the treatment of early stage tumors * Previous administration of \> 2 cycles of systemic chemotherapy as induction treatment before definitive chemoradiotherapy for early stage disease * Tumor progression during or immediately after completion of =\< 2 cycles of systemic chemotherapy as induction treatment before definitive chemoradiotherapy for early stage disease * Previous use of systemic chemotherapy or other investigational drugs for the treatment of inoperable locally recurrent or metastatic tumors (previous use of radiotherapy in this setting is not an exclusion criterion if: 1) non-irradiated target tumor lesions are present at randomization for the purpose of tumor response assessment or 2) in the absence of non-irradiated target tumor lesions, progression of the irradiated tumor lesions according to the RECIST criteria version 1.1 is documented) * Current or recent (within 30 days of first study dosing) treatment with another investigational drug or participation in another investigational study * Documented or symptomatic brain metastases and/or central nervous system metastases or leptomeningeal disease * Major surgery performed \< 28 days from treatment start * Palliative radiotherapy completed =\< 7 days from treatment start * Clinically significant (i.e. active) cardiac disease (e.g. symptomatic coronary artery disease, uncontrolled cardiac arrhythmia, or myocardial infarction within the last 6 months); any history of clinically significant cardiac failure * History of interstitial lung disease (e.g. pneumonitis or pulmonary fibrosis) or evidence of interstitial lung disease on baseline chest computed tomography (CT) scan * HIV+ patients who are not on HAART or have a CD4 count of \< 200/ul in the presence of detectable plasma viral load according to the local assay * Known history of active hepatitis B or hepatitis C infection * Serious active infection requiring intravenous (i.v.) antibiotics at enrollment * Other malignancy within the last 5 years, except for adequately treated carcinoma in situ of the cervix or squamous carcinoma of the skin, or adequately controlled limited basal cell skin cancer * Other clinically significant disease or co-morbidity that may adversely affect the safe delivery of treatment within this trial * Known hypersensitivity to any of the study drugs or excipients * Known peripheral neuropathy \> grade 1 (absence of deep tendon reflexes as the sole neurological abnormality does not render the patient ineligible) * Pre-existing hearing impairment * Patients planning for a live vaccine * Pregnant or lactating females