Taraweeh is mainly related with the Ramadan' Fasts and is prayed with little difference in numbers of Rakat, Although It was fixed in Umar R.A reign. But Muhammad S.A.W performed Taraweeh at home and in Masjid.
So we can realize its importance But where it would be more preferable -home or Mosque ?

Facts About The Origin Of Taraweeh Salah | Islamic Articles