All perfect praise be to Allaah, the Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
Fasting the Day of ‘Arafah is better than fasting the tenth of Muharram as fasting the Day of ‘Arafah atones for the sins of two years - the one that has preceded it and the one that follows it.
Fasting the tenth of Muharram atones for the sins of two years, on the other hand, only atones for the sins of one year. This is proved by the Hadeeth on the authority of Abu Qataadah, may Allaah be pleased with him, where the Prophet, sallallaahu ‘alayhi wa sallam, said: "I seek from Allaah that fasting the Day of ‘Arafah would atone for the sins of the preceding and the coming year, and I seek from Allaah that fasting the Day of ‘Aashooraa’ (Tenth of Muharram) would atone for the sins of the preceding year." Ibn Hajar said, "It is clear that fasting the Day of ‘Arafah is better than fasting the tenth of Muharram. It was said that the wisdom behind this is that the tenth of Muharram is related to Prophet Moosa (Moses), May Allaah exalt his mention, while the Day of ‘Arafah is related to Prophet Muhammad, sallallaahu ‘alayhi wa sallam, and this is why it is better."
Allaah Knows best.