Which is better for Tahajjud prayer during Ramadan: to pray at home reciting a thousand verses to obtain the reward of the "Qintareen," or to pray in congregation at the mosque reciting one juz (less than 500 verses)?

It is better to pray Tahajjud at home outside of Ramadan, based on the Prophet's (PBUH) saying: "So pray, O people, in your homes, for the best of a man's prayer is in his home, except for the obligatory prayer." This includes all supererogatory prayers, and Tahajjud is not among the prayers for which congregational prayer is sunnah, in addition to the benefit of prolonged recitation at home. As for Ramadan, there is no text that prefers one of the two situations (Tahajjud at home with extensive recitation, or Tahajjud in the mosque with the congregation) over the other.