Docetaxel or Abiraterone Acetate With ADT in Treating Patients With Metastatic Hormone Sensitive Prostate Cancer

Inclusion Criteria:

* Histologically diagnosed adenocarcinoma of the prostate.
* Radiographically confirmed metastatic disease prior to patient enrollment. Metastatic disease can be confirmed based on conventional imaging (CT, MRI, nuclear medicine bone scan) or molecular imaging (fluciclovine-positron emission tomography (PET)/CT, prostate-specific membrane antigen (PSMA)-PET/CT, Choline-PET/CT etc).
* Eastern Cooperative Oncology Group (ECOG) performance status =\< 2.
* Absolute neutrophil count (ANC) \>= 1.5 k/uL.
* Platelets \>= 100 k/uL.
* Hemoglobin \>= 9 g/dL.
* Serum total bilirubin =\< 1.5 times upper limit of normal (ULN) OR direct bilirubin =\< ULN for subjects with total bilirubin \>= 1.5 x ULN.
* Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) =\< 2.5 x ULN OR =\< 4 x ULN for subjects with liver metastases.
* Creatinine \< 1.5 x ULN OR
* Creatinine clearance \> 50 mL/min for subject with creatinine levels \> 1.5 x ULN by Cockcroft-Gault formula or standard institutional practice.
* Highly effective method of contraception for both male and female partners of subjects throughout the study and for at least 3 months after last study treatment administration if the risk of conception exists.
* Able to provide informed consent and willing to sign an approved consent form that conforms to federal and institutional guidelines.
* Recovery to baseline or =\< grade 1 Common Terminology Criteria for Adverse Events (CTCAE) version (v)5.0 from toxicities related to any prior treatments, unless adverse event (AE)(s) are clinically nonsignificant and/or stable on supportive therapy as defined by the treating physician.

Exclusion Criteria:

* No prior abiraterone or docetaxel therapy for metastatic hormone sensitive prostate cancer. Prior therapy with ADT or first generation anti-androgen receptor therapy (example: bicalutamide) is allowed.
* Completed any hormone therapy for localized prostate cancer and have recovery of testosterone (i.e. testosterone level is \>50ng/dL).
* Patients have a histologic diagnosis of small cell prostate cancer or pure squamous cell prostate cancer.
* Known brain metastases or cranial epidural disease unless adequately treated with radiotherapy and/or surgery (including radiosurgery) and stable for at least 4 weeks before first dose of study treatment. Eligible subjects must be neurologically asymptomatic and without corticosteroid treatment at the time of first dose of study treatment.
* The subject has uncontrolled, significant intercurrent or recent illness including, but not limited to, the following conditions:

  * Cardiovascular disorders:

    * Congestive heart failure New York Heart Association class 3 or 4, unstable angina pectoris, serious cardiac arrhythmias within 3 months of study enrollment.
    * Uncontrolled hypertension defined as sustained blood pressure (BP) \> 170 mm Hg systolic or \> 100 mm Hg diastolic despite optimal antihypertensive treatment.
    * Stroke (including transient ischemic attack (TIA)), myocardial infarction (MI), or other ischemic event, or arterial thromboembolic event within 3 months before first dose.
  * Other clinically significant disorders that would preclude safe study participation. As defined by the treating physician.
* Known history of testing positive for human immunodeficiency virus (HIV) and cluster of differentiation 4 (CD4) count is below 200 or known acquired immunodeficiency syndrome diagnosis.
* Known history of hepatitis B virus (HBV) or hepatitis C virus (HCV) infection at screening (positive HBV surface antigen or detectable HCV ribonucleic acid \[RNA\] if anti-HCV antibody screening test positive) and a detectable viral count at screening.
* Use of live virus vaccine within 4 weeks of the first dose of treatment or planned use while on trial for the duration of potential docetaxel treatment. Live vaccine use is acceptable after chemotherapy or for patients randomized to the abiraterone arm. There are no restrictions on inactive viruses.
* Known prior severe hypersensitivity to investigational product or any component in its formulations (National Cancer Institute \[NCI\] CTCAE v5.0 grade \>= 3).