This randomized phase III studies how well two different regimens of paclitaxel with or without trastuzumab works in treating patients with or without HER-2/Neu breast cancer that is inoperable, recurrent, or metastatic. Drugs used in chemotherapy, such as paclitaxel, use different ways to stop tumor cells from dividing so they stop growing or die. Monoclonal antibodies, such as trastuzumab, can locate tumor cells and either kill them or deliver tumor-killing substances to them without harming normal cells. It is not yet known what regimen of paclitaxel is more effective with or without trastuzumab in treating patients with breast cancer.