因为前者是标准的英语，后者是带点勉强翻译的中国味道的英语

fall off  
decrease in quantity or quality 数量或质量下降: Attendance at my lectures has fallen off considerably. 听我讲课的人已大大减少了. 
* It used to be my favourite restaurant but the standard of cooking has fallen off recently. 那是我以前最喜欢的饭馆, 但近来烹饪水平已大不如前了.

fall down  
be shown to be false or inadequate; collapse 显示不实或不足; 崩溃; 失败: The plan fell down because it proved to be too expensive. 这项计划因费用过高而告吹. 
fall down on sth (infml) fail to do sth properly or successfully 没有把某事做好: fall down on one's promises 未履行自己的诺言 
* He fell down on the job. 他未能把这件工作做好.