Inclusion Criteria:

* Histologically or cytologically confirmed prostate cancer
* Metastatic disease
* On androgen-deprivation therapy for \< 120 days
* Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0-2

* PS 2 eligible only if decline in PS is due to metastatic prostate cancer
* Absolute neutrophil count ≥ 1,500/mm\^3
* Platelet count ≥ 100,000/mm\^3
* Bilirubin ≤ upper limit of normal (ULN)
* Alanine aminotransferase (ALT) ≤ 2.5 times ULN
* Creatinine clearance ≥ 30 mL/min
* Prothrombin time (PT) and international normalized ratio (INR) ≤ 1.5 times ULN (unless on therapeutic anticoagulation)
* Partial thromboplastin time (PTT) ≤ 1.5 times ULN (unless on therapeutic anticoagulation)
* Fertile patients must use effective contraception
* At least 4 weeks since prior major surgery and recovered from all toxicity prior to randomization
* Prior adjuvant or neoadjuvant hormonal therapy allowed provided the following are true:

* Therapy was discontinued ≥ 12 months ago AND there is no evidence of disease, as defined by 1 of the following:

* PSA \< 0.1 ng/dL after prostatectomy plus hormonal therapy
* PSA \< 0.5 ng/dL and has not doubled above nadir after radiotherapy plus hormonal therapy
* Therapy lasted no more than 24 months

* Last depot injection must have expired by the 24-month mark
* Prior palliative radiotherapy allowed if commenced within 30 days before starting androgen deprivation
* Anti-androgen therapy allowed as single-agent therapy ≤ 7 days before medial castration to prevent flare
* More than 30 days (or 6 half-lives) (whichever is longer) since prior participation in another clinical trial
* Concurrent participation in nontherapeutic trials allowed
* Concurrent antiandrogen therapy (e.g., bicalutamide or flutamide) allowed, but not as sole hormonal therapy

Exclusion Criteria:

* Prostate-specific antigen (PSA) level has risen and met criteria for progression from its lowest point between the start of androgen-deprivation therapy and randomization
* Prior malignancy in the past 5 years except for basal cell or squamous cell carcinoma of the skin

* Other malignancies that are considered to have low potential to progress (e.g., grade 2, T1a transitional cell carcinoma) may be allowed if approved by study chair
* Peripheral neuropathy \> grade 1
* History of severe hypersensitivity reaction to docetaxel or other drugs formulated with polysorbate 80
* Active cardiac disease, including the following:

* Active angina
* Symptomatic congestive heart failure
* Myocardial infarction within the past 6 months
* Prior chemotherapy in adjuvant or neoadjuvant setting
* Prior hormone therapy in the metastatic setting
* Concurrent 5-alpha reductase inhibitors
* Simultaneous enrollment on Cancer and Leukemia Group B (CALGB) 90202