According to the Gemara Rosh Hashana (17b) the recitation of the 13 attributes of God leads to forgiveness:
א"ר יוחנן אלמלא מקרא כתוב אי אפשר לאומרו מלמד שנתעטף הקב"ה כשליח צבור והראה לו למשה סדר תפלה אמר לו כל זמן שישראל חוטאין יעשו לפני כסדר הזה ואני מוחל להם
It seems strange to me that God would be more affected by particular words.
Do any Rishonim address this?
Note: evidence that Rishonim reject this Gemara would be an appropriate answer.
Clarification: The question seems clear, but I will reiterate: Granted that God responds to prayer, but why should he be particularly affected by particular words; its not like He is going to get emotional over them. If instead they are simply meant as prayer (rather than as a means of effecting some particular change in God, emotional or otherwise) then why would some words be more effective than others? Prayer is ultimately עבודה שבלב; an internal process, even if one expresses it externally.