Both regular and digital x-rays use the same type of radiation. With repeated high dose exposures over a short period of time, this radiation dose does have the potential to be harmful. This is why strict regulations are in place to ensure the amount of radiation being used is within the limits of what your body can absorb and dissipate without any negative side effects.
The main difference between digital and conventional x-rays is the amount of radiation required to get a similar quality image. With direct digital x-rays the amount of radiation can be reduced by up to 90% depending on the type of x-ray taken and which type of conventional film it is being compared to.