How directly you feel the ground through your sole. Thin, flat rubber soles give you plenty of it; cushioning trades feedback for protection.
Parkour is minimalist: the shoe is effectively your only piece of equipment, and it's also where technique turns into contact. A thin, flat full-rubber sole tells you exactly where your foot landed on a rail or a ledge, and a softer rubber compound grips better. The catch is the same construction: it passes the impact of a drop through more or less unfiltered. That's why beginners are usually better served with some cushioning at bigger heights, while experienced traceurs deliberately choose less padding to get more feedback. Worth being straight about: this is community experience, not established evidence — there is essentially no parkour-specific research on shoe cushioning versus landing force. What is well documented is that technique lowers the forces. You can't buy your way out of a landing problem.