RADIANT: A Study of Radium-223 Dichloride (Xofigo) vs Enzalutamide or Abiraterone (ARPIs, Androgen Receptor Pathway Inhibitors) in Patients With Prostate Cancer That Has Spread to the Bones (mCRPC, Metastatic Castration-Resistant Prostate Cancer)

Inclusion Criteria:

* Participants who have histologically confirmed adenocarcinoma of the prostate.
* Participants with mCRPC progressing on/after one line of an approved ARPI (eg. abiraterone, enzalutamide, apalutamide, or darolutamide, after being treated for at least 3 months) in an authorized prostate cancer indication.
* One prior taxane treatment regimen (at least 2 cycles) for metastatic prostate cancer (mHSPC and mCRPC) or refusal or ineligibility of such a regimen.
* Prostate cancer progression documented by PSA according to the Prostate Cancer Working Group 3 (PCWG3) criteria or radiological progression according to RECIST, version 1.1.
* At least 2 bone metastases on bone scan within 4 weeks prior to randomization with no current or history of lung, liver, other visceral, and / or brain metastasis.
* Symptomatic prostate cancer. A worst pain score (WPS) of at least 1 on the Brief Pain Inventory-Short Form (BPI-SF) Question #3 (worst pain in last 24 hours). This is to be assessed once during the Screening period.
* Maintenance of medical castration or surgical castration with testosterone less than 50 ng/dL (1.7 nmol/L). If the participant is being treated with luteinizing hormone releasing hormone (LHRH) agonists or antagonists (participant who has not undergone orchiectomy), this therapy must have been initiated at least 4 weeks prior to randomization and must be continued throughout the study.
* Participants must be on a BHA treatment, such as bisphosphonates or denosumab treatment unless such treatment is contraindicated or not recommended per investigator's judgement and inclusion is agreed to by the medical monitor.
* Eastern Cooperative Oncology Group performance status (ECOG PS) 0 or 1.
* Life expectancy ≥ 6 months.
* Able to swallow abiraterone and prednisone/prednisolone or enzalutamide as whole tablets/capsules.
* Laboratory requirements:

  * Absolute neutrophil count (ANC) ≥ 1.5 x 10\^9/L
  * Platelet count ≥ 100 x 10\^9/L
  * Hemoglobin (Hb) ≥ 9.0 g/dL (90 g/L; 5.6 mmol/L)
  * Total bilirubin level ≤ 1.5 x institutional upper limit of normal (ULN) (except for participants with documented Gilbert's disease)
  * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 2.5 x ULN
  * Creatinine ≤ 1.5 x ULN or estimated glomerular filtration rate (eGFR) ≥ 30 mL/min/1.73 m\^2 as calculated using the Cockcroft-Gault equation
  * International normalized ratio (INR) of prothrombin time (PT; PT-INR) and partial thromboplastin time (PTT) ≤ 1.5 times the ULN. Participants treated with warfarin or heparin will be allowed to participate in the study if no underlying abnormality in coagulation parameters exists per prior history; weekly evaluation of PT-INR / PTT will be required until stability is achieved (as defined by local standard of care and based on pre-study PT-INR / PTT values)
  * Serum albumin \> 30 g/L
  * Serum potassium ≥ 3.5 mmol/L
* Capable of giving signed informed consent

Exclusion Criteria:

* Active infection or other medical condition that would make prednisone / prednisolone (corticosteroid) use contraindicated.
* Any chronic medical condition requiring a higher dose of corticosteroid than 10 mg prednisone / prednisolone equivalent daily for more than 2 months.
* Pathological finding consistent with tumors with predominant neuroendocrine features or small cell carcinoma of the prostate.
* History of osteoporotic fracture
* History of visceral metastasis, or presence of visceral metastasis detected by screening imaging examinations.
* History of or known brain metastasis.
* Malignant lymphadenopathy exceeding 3 cm in short-axis diameter.
* Other malignancy treated within the last 3 years (except non-melanoma skin cancer or low-grade superficial bladder cancer)
* Imminent spinal cord compression based on clinical findings and / or magnetic resonance imaging (MRI). Participants with history of spinal cord compression should have completely recovered.
* Uncontrolled hypertension (systolic blood pressure ≥ 160 mmHg or diastolic blood pressure ≥ 95 mmHg). Participants with a history of hypertension are allowed provided blood pressure is controlled by anti-hypertensive treatment.
* Active or symptomatic viral hepatitis
* History of pituitary or adrenal dysfunction
* Any other serious illness or medical condition such as, but not limited to:

  * Any infection ≥ National Cancer Institute Common Terminology Criteria for Adverse Events (NCI-CTCAE) version 5.0 Grade 2
  * Clinically significant heart disease as evidenced by myocardial infarction, or arterial thrombotic events in the past 6 months, severe or unstable angina, or New York Heart Association (NYHA) Class II to IV heart disease or cardiac ejection fraction measurement of \<50% at baseline
  * Current clinical evidence of any uncontrolled cardiac arrhythmia
  * Crohn's disease or ulcerative colitis
  * Bone marrow dysplasia
  * Moderate and severe hepatic impairment (Child-Pugh Classes B and C)
  * Unmanageable fecal incontinence.
* Any condition, which in the opinion of the investigator would preclude participation in this trial (eg, history of seizure).
* Hypersensitivity to the active substances or to any excipients of radium-223 dichloride, or abiraterone acetate or enzalutamide.
* Prior therapeutic systemic radiation with any radiopharmaceutical medication for the treatment of prostate cancer, including but not limited to lutetium-177, strontium-89, samarium-153, iodine-131, rhenium-186, rhenium-188, or radium-223. Radiopharmaceutical compounds used for diagnosis purposes only are allowed.
* Prior hemibody external radiotherapy is excluded. Participants who received other types of prior external radiotherapy are allowed provided that the bone marrow function is assessed and meets the protocol requirements for Hb, ANC, and platelet count.
* Blood transfusion or erythropoietin stimulating agents 4 weeks prior to Screening and during the whole Screening period before randomization.
* Excessive intake of biotin above the recommended daily dose of 30 μg. Biotin is found in multivitamins, including prenatal multivitamins, biotin supplements, and dietary supplements for hair, skin, and nail growth at levels that may interfere with laboratory tests.
* Prior administration of an investigational therapeutic for CRPC.
* Previous (within the last 4 weeks of randomization) or concurrent participation in any interventional clinical study with investigational study drug administration.