I assume you mean automated systems, not paying someone to answer
emails versus answering the phone.
It comes down to implementation. But don't expect more than a 10%
drop overall. And that is if you've done really well.
There are a lot of reasons for this, but the primary one is that if
you answer every possible issue on the site, it becomes hard to find
the right answer. And if you only answer the big ones, you still get
all the questions you didn't answer.
On top of this, there are many reasons someone needs to talk to a
real person.