When you type in the word, many IMEs will also display a side dictionary with supplemental information. On my PC, for 川 is says: （一般的）川が流れる、川を渡る、三途（さんず）の川. For 河, it says: （限定的）（外国の）大きな川。→川.
Hence, 川 is general while 河 is limited in usage and typically represents (foreign) large rivers. In addition, 河 often refers to the Yellow River (黄河).
That being the case, do not forget that "kawa" is a Japanese word. It existed before the introduction of kanji to Japan. Chinese has multiple words for "river". Japanese "kawa" does not distinguish between 川 or 河 like Chinese. It is the this application of Chinese to express Japanese words that has created this problem.