Powder detergent is cheaper and has a longer shelf life. You can also easily customise the amount to use per load. It works fantastic on heavily stained clothes as well. However, some powder detergent is a bit difficult to dissolve in cold water and needs to be kept dry.
Liquid detergent works better in cold water. It is also more suitable for handwashing. Liquid detergent removes oil and stains with ease too. However, this option is a bit pricier than powder.