As usual the answer is IT DEPENDS
It depends mainly on processes involved (energy and chemical consumption) - here you can find good and bad solutions for both sea water and ground water desal - and waste streams generated and how they are treated/disposed.
Waste streams are very saline, often have significant chemical concentrations and occur in large volumes (usually a similar amount as desalinated water). In inland areas (brackish groundwater desal) this is usually a challenge, since this wastestream often cannot be pumped back to the aquifer. Big evaporation ponds are frequently used instead. At the sea, one can often design a proper hydraulic solution that disperses the brine effectively in the sea. Yet, in the mixing zones high salinity and chemical concentrations can still create severe damages to some sensitive ecospheres.
Doing a proper assessment, followed by a proper engineering design and the use of davanced technologies should overcome the challenges listed above.