问题本身就有问题，你说“名词 attempt 后接不定式 to do sth 和 of doing sth 有区别吗”，其实用作名词的 attempt 后面只能接不定式 to do sth，不能接 of doing sth。如：

They made an attempt to land. 他们试图着陆。

She made every attempt to help us. 她做了一切努力来帮助我们。

He made a diligent attempt to learn Russian. 他勤奋地学俄语。

不过，如果将介词改为 at 则完全可以，即可以接 at doing sth。如：

They made no attempt at escaping. 他们没有试图逃跑。

Their first attempt at climbing the mountain failed. 他们的初次登山尝试以失败告终。

He made an attempt at appearing to be in control. 他试图显出掌握着大局的样子。