Tarawih prayer is Sunnah Mu'akkadah for men and women since the blessed Messenger said:
'The month in which Allah has prescribed for you fasting and I have initiated for you the night prayer.Whoever fasts in it and prays with sincerity and faith, sins leave him clean and the day his mother gave birth to him'. (Ibn Maja)
The Tarawih with congregation is more virtuous since `Umar (r) established it with the congregation and the congregational prayer is a communal Sunnah. If no one prayed it in the Mosque all the people have sinned and missed the Sunnah.