Are stiff or flexible wrist wraps better?

It depends on the lift. According to mainstream reviewers, stiff wraps provide maximum support for heavy bench, squats, and overhead pressing but can feel restrictive and need a break-in period, while flexible/soft wraps are more comfortable for high-rep work, CrossFit-style training, and Olympic lifts. Some brands, like Rip Toned, sell both stiffness levels.