I have never completely thrown out code. Even when going from a foxpro system to a c# system.
If the old system worked then why just throw it out?
I have come across a few really bad system. Threads being used where not needed. Horrible inheritance and abuse of interfaces.
It is best to understand what the old code is doing and why it is doing it. Then change it so that it is not confusing.
Of course if the old code doesn't work. I mean can't even compile. Then you might be justified in just starting over. But how often does that actually happen?