This randomized phase II trial studies how well temozolomide and capecitabine work compared to standard treatment with cisplatin or carboplatin and etoposide in treating patients with neuroendocrine carcinoma of the gastrointestinal tract or pancreas that has spread to other parts of the body (metastatic) or cannot be removed by surgery. Drugs used in chemotherapy, such as temozolomide, capecitabine, cisplatin, carboplatin and etoposide, 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. Certain types of neuroendocrine carcinomas may respond better to treatments other than the current standard treatment of cisplatin and etoposide. It is not yet known whether temozolomide and capecitabine may work better than cisplatin or carboplatin and etoposide in treating patients with this type of neuroendocrine carcinoma, called non-small cell neuroendocrine carcinoma.