UsePolyester is used in a wide range of sportswear because it is so durable and quick drying.Nylon is most commonly used by yoga and innerwear brands. This is because it is soft, smooth and feels nice next to skin.
FeelDrier and rougherSofter and smoother
CostCheaperMore expensive
DyestuffDyed using disperse dyes.Dyed using acid dyes.
Dyeing and colorfastnessAbsorbs dyestuffs well.Does not hold color well. Dyed nylon fades quicker than polyester in sunlight.
Abrasion resistancePerforms betterPerforms worse
DurabilityLess durable than nylon but more durable than natural fiber.More durable, stronger and stretchier than polyester.
Reaction to heatMore durable in high heat.Cannot be processed under high heat.
Reaction to waterWater retention ratio: 0.4
Polyester is hydrophobic and quick drying.
Water retention ratio: 4
Nylon absorbs more water than polyester.
CareBoth nylon and polyester are easy to care for. They shouldn’t be dry cleaned but they can be ironed and tumble dried on a low heat. 


Source: https://www.eysan.com.tw/difference-between-polyester-and-nylon-fabric/