Learn Russian: Мне нужно сравнивать оба документа.

The word оба (both) works just like the number two (два). It requires the following noun to be in the genitive singular. Since документ is masculine, it takes the genitive singular ending -а, becoming документа.

Would the word for 'both' change if I were comparing feminine nouns?

Yes! For feminine nouns, you must use обе instead of оба. For example, if you were comparing two versions (версия), you would say обе версии.

Why use the imperfective сравнивать instead of the perfective сравнить here?

Using the imperfective сравнивать suggests that comparing these documents is an ongoing process, a continuous task, or part of your general routine. If you just needed to compare them once to achieve a single, final result, you would use the perfective сравнить.

Why does the sentence start with Мне instead of Я?

To express 'I need' using нужно (it is necessary), the person experiencing the need must be in the dative case. Therefore, я (I) changes to мне (to me), making the literal translation 'to me it is necessary to compare'.