Can anybody summarize differences and usage scope between them?
I read SO articles,
- ShouldBeEquivalientTo(): ShouldBeEquivalentTo() is intended to be used for comparing complex object graphs rather than the primitive types part of the .NET framework.
 - Should().BeEquivalentTo(): individual items Equals() implementation to verify equivalence and has been around since version 1. The newer ShouldBeEquivalenTo() introduced in FA 2.0 is doing an in-depth structural comparison and also reporting on any differences.
 - Should().Be(): cannot find.
 
In my humble understanding, ShouldBeEquivalientTo() and Should().BeEquivalentTo() work similar if Should().BeEquivalentTo() does in-depth comparison.