Is a screw or push-in terminal better for vibrating environment?
Push-in or 'cage-clamp' terminals have been around for several decades now and are a reliable solution for connections in general and vibration-proof contacts in particular. Some of the electricians where I work still prefer the hand-tightened screw terminal but some of our machine builders have switched to cage-clamp, where possible, to eliminate problems with terminals vibrating loose during road transportation.

Cage-clamp terminals are made by many companies.



Figure 1. Wago cage-clamp terminals.

Some of the terminals require a 'just right' screwdriver to release the cage properly. (Some screw terminals require the right tool too.)



Figure 2. Cage clamp and wire showing excellent contact area.

(Photos used previously in my answer to another question.)