Hi Natalie, I think they have some difference, but almost they are same in use. お伺いします：humble language * this word also include the mean "to go to your place modestly" おたずねします：Polite language * "to ask something politely"

I will explain roughly. 伺う ① a humble word of 聞<き>く／尋<たず>ねる<to ask/inquire>. ② a humble word of 訪<たず>ねる<to visit>. 尋ねる ① to ask/inquire お伺いします I (will) ask/ inquire you. ［very humble＋polite］ 伺います I (will) ask/ inquire you. ［humble＋polite）］ お尋ねします I (will) ask/ inquire you. ［humble＋polite］ 尋ねます I will ask/ inquire (my company).［polite］ ※ShiInne wrote the following. お伺いします：humble language おたずねします：Polite language There are some mistakes. Both of them are humble and polite expressions. お～する is a humble expression. ます is a auxiliary verb to add politeness. And 伺う is already a humble word itself. ※I will correct your Japanese on your introduction page（http://www.italki.com/user/1256584）. 現地の日本の話者と私の日本人を訓練したいです! 日本人（Japanese people）→日本語（Japanese language）

※There is not a message box on your page. So I will write here. This correction site is intended to have other people correct errors of the Japanese sentence that you wrote. It is not the thing which you end up by being satisfied with your writing. The person to correct corrects it hard. At least I am so. The expense is not caused there. It is a volunteer. It is courtesy that the person who contributed the original gives thanks for the person who corrected. You may not feel good that a lot of things which you wrote are corrected. However, it is what you should be rather pleased with. Because your Japanese becomes better (more natural) and it's useful for you. You showed no reaction to the next article which I corrected. I am interested whether my correction was helpful for you. I will be happy if I will be able to get your reply. http://www.italki.com/question/331004(this page)