This randomized phase II trial studies how well robotic radical cystectomy (RRC) or open radical cystectomy (ORC) works in treating patients with bladder cancer. Cystectomy is a surgical procedure to remove all or part of the bladder (the organ that holds urine) or to remove a cyst (a sac or capsule in the body). In RRC, the the surgeon makes small cuts in the abdomen and uses a thin, lighted instrument with a camera attached called a scope. With the help of a robot, the surgeon removes the bladder and other nearby structures. In ORC, the surgeon makes a cut into the lower abdomen to expose the urinary tract in order to remove the bladder and nearby structures. It is not yet known whether RRC or ORC has fewer complications, better quality of life, and faster recovery time in treating patients with bladder cancer.