 This randomized phase II trial studies the side effects and how well giving leuprolide acetate or goserelin acetate works compared to observation in treating patients with high-risk prostate cancer who have undergone radical prostatectomy. Androgens can cause the growth of prostate cancer cells. Antihormone therapy, such as goserelin acetate and leuprolide acetate, may lessen the amount of androgens made by the body and thus control prostate cancer growth. Many times, after surgery, the tumor may not need more treatment until it progresses. In this case, observation may be sufficient. However, in some prostate cancers there is a chance that tumors can re-grow despite surgery based on certain high risk features. 