Is it better to shoot professional still life and professional stop-motion animation with constant light or flash?

That's right, because the constant light needs an expensive model, and the color temperature is very good, while the flashing light can be as long as it is very cheap; But flashing lights are always less convenient than constant lights, and can only achieve preview effect.

Stroboscopic

... very painful.

If you pursue color temperature, I'll give you a method used by an evil expert. Go to the auto parts to buy a set for the car.

xenon lamp

That color temperature can reach a high level, and it is still accurate, but the power supply needs someone who knows how to change it.