This randomized phase III trial studies paclitaxel and carboplatin see how well they work compared with paclitaxel and ifosfamide in treating patients with fallopian tube, or peritoneal cavity cancer that is newly diagnosed, persistent, or has come back (recurrent). Drugs used in chemotherapy, such as paclitaxel, carboplatin, and ifosfamide, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. It is not yet known whether paclitaxel is more effective when given with carboplatin or ifosfamide in treating patients with uterine, ovarian, fallopian tube, or peritoneal cavity cancer.