According to my knowledge build is doing exactly what new does, additionally it updates the Collection with which new Model is associated. So after using build to create new user shout, you could save new shout in persistence layer by calling save method on user:
shout = user.shouts.build(shout_parameters)
# now user.shouts contain new shout
# and you can run .save method on either user or shout
shout.save
# or
user.save
while with new you cannot save new shout in persistence layer by saving user. You have to call save method on new Shout instance:
shout = user.shouts.new(shout_parameters)
shout.save
Hope that makes sense