In which teapot the water is more likely to heat up in a new or old one, on the walls of which there is scale?

The thermal conductivity of the scale is much worse than the thermal conductivity of the heating element, therefore heat transfer to water will be less efficient and the heating element may burn out. Without scale, heat transfer from the heating element to the water is faster, so the water heats up earlier. And the kettle will last longer if it is regularly descaled.