Which is better: performing Tarawih prayer at home with short surahs while reciting the Qur’an, or at the mosque? And does the reward for performing Tarawih prayer at home equal its reward at the mosque?

A woman's prayer in her home is better than her prayer in the mosque. However, she is permitted to pray in the mosque provided that there is no fitnah (temptation/strife), suspicion, or any other religiously prohibited matter. There may be some advantages associated with praying in the mosque that make it better, such as the presence of a devout, influential reciter as an Imam, or a teacher who instructs people in what a Muslim cannot afford to be ignorant of, or if there is distracting noise in the home.