The statement is true given that X is a normal good.In general, the compensated demand curve is somewhat less responsive to price changes than is the uncompensated curve for a normal good. This is because the latter reflects both substitution(SE) and income effects(IE) of price changes,where as the compensated curve reflects only substitution effects.

Thus for a given price increase, the fall in demand is more in case of a marshallian demand function because both SE and IE are at play.In case of a price fall, the demand rises morel for marshallian demand function for the same reason as mentioned above, resulting in a flatter Marshallian demand curve and a steeper compensated demand curve.