There is absolutely no functional difference between a red and black PSP (PlayStation Portable)—the hardware, performance, and features are identical. The choice comes down entirely to aesthetics, practical preferences, and what's available on the used market.
Choose black for a low-maintenance, timeless look that hides wear. Choose red if you want personality, easier visibility, and don't mind wiping it down occasionally. Either way, buy the best-condition model you can afford—the gameplay experience is identical.