Maliki and Hanafi – Silent recitation of qunoot is preferred as it is a du’a. Quran ادْعُوا رَبَّكُمْ تَضَرُّعًا وَخُفْيَةً ۚ إِنَّهُ لَا يُحِبُّ الْمُعْتَدِينَ – 7:55 Call upon your Lord in humility and privately; indeed, He does not like transgressors. It is the same reason why Ameen is said silently after Fatihah in salaah.
Hambali and Shafi’ – said Aloud.
Note: Here the difference is only a matter of preference rather than permissibility.