I can't understand how one might be used instead of the other.
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なさる, whose polite form is なさいます, is 尊敬語｛そんけいご｝ 'honorific language', whereas いたす, whose polite form is いたします, is 謙譲語｛けんじょうご｝ 'humble language'.
You would use なさる to show respect for somebody performing an action, whereas いたす humbles your own actions in respectful environments. Both are ultimately about respect, of course.
お飲み物はどうなさいますか。= 'What are you going to do about the drinks?'
お飲み物はどういたしますか。= 'What shall I do about the drinks?'