Both Super Capacitors and Hybrid capacitors do not show good phase response. Non of them can achieve near -90 degree phase and phase is not constant over audio frequency range(20Hz to 20KHz). Definitely these capacitor can dominate or change sound of the analogue circuits!  

​All measurements were taken on same test equipment. Result may vary with different test condition.
CDE DCNS 1F 2.7Vdc:
Eaton HV 1F 2.7Vdc:
Eaton KR 0.22F 5.5Vdc:
IOXUS 350F 2.7Vdc:
IOXUS 3000F 2.7Vdc:
This capacitor is unique. Phase is near 0 degree (not capacitive, not inductive) and somewhat consistent up to 1KHz.
Nichicon JUWT 1F 2.7Vdc:
Panasonic EEC 0.22F 5Vdc:
KEMET FC 0.047F 5.5Vdc:
Evans THS3030303 300,000uF 50Vdc:
tantalum hybrid capacitors
Phase is EVERY WHERE! Definitely this cap will dictate the sound!