When we have new in C#, that personally I see only as a workaround to override a property that does not have a virtual/overridable declaration, in VB.NET we have two "concepts" Shadows and Overloads.
In which case prefer one to another?
There are three closely related concepts; overriding, shadowing and overloading.
Overriding is when you make a new implementation for a virtual method.
Shadowing is when you make a new non-virtual implementation for a method.
Overloading is when you add a method with the same name but different parameters.
All three concepts are available both in C# and VB.