An other big advantage is that one doesn’t need Cord End terminals to end a flexible (stranded) cable.
Flexible cable in a screw clamp will losen after a while because the thin wires will reorganise themselves. Especially under influence of vibrations. In Belgium it’s even not aloud to use flexible cable in a screw clamp without Cord End terminals.
Flexible cables in cage clamps give no problem since the spring permanently tightens the cable.
Cage clamps are also faster, but they are more expensive.
I have only used WAGO cage clamps (up to 95mm²) and have had no negative experience with them.