Weekdays, by the repetition of the Amida, it is the Ashkenazik custom for the chazzan to say an abridged version of Birkat cohanim. The Artscroll siddur says the chazzan is to bow to the right side during the recitation of "Yevarechecha Hashem Veyishmerecha," to bow to the left hand side during the recitation of "Ya'er Hashem panev eilecha vichuneka" and to bow forward by the last verse of "Yisa Hashem panev eilecha veyasem lecha shalom."
When it comes to the end of the Amida, the Artscoll Siddur brings down that one should first bow to the left side during the "Oseh Shalom," then to the right by "Hu yaaseh shalom..." and finally forward during the conclusion.
Why the different order in each?