Equinox is a newer ship and the water will probably be just fine.
I used to answer these types of questions by saying: "The ship's water is as good or better than any bottled water or public water supply. Don't bother with bottled water."
While this statement is usually true I have found instances of ships that have an off taste and/or discoloration to their water. The Carnival Pride, HAL Statendam, Radiance of the Seas and Celebrity Century have all had off tasting and/or brown water that made me not want to drink it. The water was perfectly safe but not nice to drink.
The problems occur when the plumbing becomes older and sediment builds up in pipes. The water in the desalination tanks is just fine but it picks up "stuff" on the way to your faucet.
So: If you are fussy about water and sailing on a ship older than four or five years then you may want to use bottled water.