Is saying "يا أرحم الراحمين" (O Most Merciful of the merciful) in supplication and intimate converse incorrect, or is it better to say "يا رحمن يا رحيم" (O Most Gracious, O Most Merciful)?

Supplicating with "Most Merciful of the merciful" is مطلوب (sought after) and established in the Quran and Sunnah. In the Quran, Allah Almighty says: "He said, 'My Lord, forgive me and my brother and admit us into Your mercy, for You are the Most Merciful of the merciful.'" (Al-A'raf: 151). In the Sunnah, Al-Bukhari reported in Al-Adab Al-Mufrad from Abu Hurairah that the Prophet, peace and blessings be upon him, said to a man who was hugging a child: "Do you have mercy on him?" He said: "Yes." Then he said: "Allah is more merciful to him than you, and He is the Most Merciful of the merciful."