It makes a difference not having to download all the email and then sort it, as avast will have to scan all that email, mailwasher is very effective at what it does detect spam, it is very flexible and configurable not unlike avast.
Your selective quote you posted above doesn't have anything to do with being on dial-up (I would recommend it even for broadband users) but having avast Internet Mail ignore mailwasher.exe, avoiding duplicate scanning by avast.
