The acid anhydride gives the acid as a by product whereas the acid chloride gives HCl as a by product which is easier to seperate from the product you want.
The acid chloride is also more reactive and hence the reaction is faster.
using acid + alcohol to make ester is a poor way to do it, its an equilibrium reaction so you end up with a mixture of products and a poor yield of ester, using the acid chloride instead of the carboxylic acid, the reaction goes to completion, its not an equilibrium reaction.