Are stiff wraps or flexible wraps better?

It depends on your goal. Stiff, heavy-duty wraps (the style favored by Iron Infidel, PR, and Gymreapers' competition line) provide the most stability for max-effort bench and overhead work but feel restrictive for higher-rep bodybuilding sets. Softer, more elastic wraps are more comfortable for general training and Olympic-style lifts. Specialist subreddit consensus is that most lifters benefit from owning one of each rather than compromising.