face up to responsibility,face responsibility有区别吗？

在这里没有！
face up to responsibility＝face responsibility“敢于承担责任”
face up to“敢于承担责任”“正视（历史）等”“面对现实”

刚才看错了。以为是face 和face up to的比较。

回答的这么好，怎么半天一点分都没有啊？

face up to
accept the fact that, meet something or someone without shrinking
face up to
勇敢地对付; 面对事实 一般不和responsibility一起用。

Face difficulty, responsibility and challenge with brave and calm attitude.
坦然面对困难，敢于承担责任，勇于接受挑战。