OBJECTIVES: I. Compare the objective response rate, duration of remission, overall survival, and quality of life of patients with progressing regional or metastatic transitional cell carcinoma (or mixed histologies with a component of transitional cell carcinoma) of the urothelium treated with methotrexate, vinblastine, doxorubicin, and cisplatin vs carboplatin and paclitaxel. II. Compare the relative toxic effects of these treatment regimens in this patient population.