Hindus do prefer birth anniversaries (jayanti) over death anniversaries (punya tithi). However, we can qualify this by saying most Hindu festivals are about the birth of a God (Ram’s birth, Krishna’s birth, Hanuman’s birth, Garuda’s birth) or about the death of a demon (killing of Mahisha by Durga, killing of Ravana by Ram, killing of Naraka by Krishna). Both these events, birth of a god and death of a demon, are seen as evoking positivity.
This is very different from the Christian practice of mourning the death of Jesus Christ (Good Friday), and commemorating the martyrdom of saints, or the Shia Muslim practice of mourning the death of the Prophet’s son-in-law’s family (Muharram).
The reason for this is that birth is seen as auspicious and death as inauspicious in Hindu worldview. Ramayana is more sacred than Mahabharata, because Ramayana describes the birth of Ram, while Mahabharata does not describe the birth of Krishna. More value is placed on Bhagavata Purana where Krishna’s birth is described.
All religions have something like “all soul’s day” where the living remember the dead. In Hinduism, this is the fortnight of “pitr paksha” when rituals are performed for the dead. But there is a difference. The dead in Christianity and Islam are in purgatory, having lived their life in full, waiting for the Final Day of Judgment. The dead in Hinduism are waiting for rebirth. But by and large, association with death is shunned in Hindu traditions, especially when compared with the value placed on death in other religions.
In Islamic and Christian traditions, death is valued and so tombs and graves become monuments. Traditionally, in most Hindu communities, no relic of the dead was kept in or around the house. All things that touch death were seen as polluting and inauspicious. In later Hindu monastic tradition, the body of dead teachers was buried and a Tulsi plant grown above the grave. Though it is not worshipped, the place of burial is thus marked. This practice may have come from Buddhists who would keep relics (tooth, hair, bones) of great teachers, after their cremation.