How to compare two Json objects using C#

I did a bit more digging and was able to find out why the OP's test code doesn't run as expected. I was able to fix it by installing and using the FluentAssertions.Json nuget package.

One important thing:

Be sure to include using FluentAssertions.Json otherwise false positives may occur.

Test code is the following:

using FluentAssertions;
using FluentAssertions.Json;
using Newtonsoft.Json;
using Newtonsoft.Json.Linq;
using NUnit.Framework;

[TestFixture]
public class JsonTests
{
    [Test]
    public void JsonObject_ShouldBeEqualAsExpected()
    {
        JToken expected = JToken.Parse(@"{ ""Name"": ""20181004164456"", ""objectId"": ""4ea9b00b-d601-44af-a990-3034af18fdb1%>"" }");
        JToken actual = JToken.Parse(@"{ ""Name"": ""AAAAAAAAAAAA"", ""objectId"": ""4ea9b00b-d601-44af-a990-3034af18fdb1%>"" }");

        actual.Should().BeEquivalentTo(expected);
    }
}

Running the test:

Consider using the JToken.DeepEquals() method provided by Newtonsoft. It would look somewhat like this, regardless of which testing framework you're using:

Console.WriteLine(JToken.DeepEquals(InstanceObjActual, InstanceObjExpected));
// false

Made a non-recursive method which will remove twins - idea is to remove same elements from very similar JSONs, so that there will remain only different nodes in each object:

public void RemoveTwins(ref BreadthFirst bf1, ref BreadthFirst bf2) {
    JsonNode traversal = bf1.Next();
    Boolean removed = false;
    do {
        if (!removed) {
            if (bf2.Current != null) while (bf1.Level == bf2.Level && bf2.Next() != null) ;
            if (bf2.Current != null) while (bf1.Level != bf2.Level && bf2.Next() != null) ;
            else bf2.Current = bf2.root;
        }
        else traversal = bf1.Next();
        if (bf2.Level < 0) bf2.Current = bf2.Root;
        do {
            removed = bf1.NextAs(bf1.src, bf2, bf2.src);
            if (removed && bf1.Orphan && bf2.Orphan) {
                JsonNode same = bf1.Current.Parent;
                traversal = bf1.RemoveCurrent();
                same = bf2.Current.Parent;
                bf2.RemoveCurrent();
                bf1.UpdateLevel();
                bf2.UpdateLevel();
                if (traversal == null
                || bf1.Root == null || bf2.Root == null
                || (bf1.Level == 0 && bf1.Current.NodeBelow == null)) {
                    traversal = null;
                    break;
                }
            } else
            if (!removed) {
                break; 
            } else removed = false;
        } while (removed);
        if (!removed) traversal = bf1.Next();
    } while (traversal != null);
}

Complete code + parser on my GitHub (profile or below).
Older CSV version which also sorts input mentioned in my question here How to compare big JSON's? (new one does not, so it could be very slow when one of objects has reversed order - it would be easier to sort during parsing or at least compare both neighbours of twins as first search step)