What is the difference between "Subhanaka Rabbi al-Azim" (Glory be to You, my Lord, the Most Great) and "Subhana Rabbi al-Azim" (Glory be to my Lord, the Most Great) during bowing (ruku') and prostration (sujud), and which of them is more correct in prayer?

The correct form for the glorification in bowing (ruku') is "Subhana Rabbiyal-Azeem (Glory be to my Lord, the Most Great)," as narrated in the hadith of Hudhayfah (may Allah be pleased with him) concerning his prayer with the Messenger of Allah, peace and blessings be upon him. The other form, "Subhanaka Rabbiyal-Azeem (Glory be to You, my Lord, the Most Great)," has not been reported for the glorification in bowing.