If you just want to do a one time compare on 2 json strings there's this resource on the web
http://tlrobinson.net/projects/javascript-fun/jsondiff
In Json.Net there is a DeepEquals available on JToken so.
var json1 = JToken.Parse(jsonString1);
var json2 = JToken.Parse(jsonString2);
var jsonEqual = JToken.DeepEquals(json1, json2);
If you want to do exactly what you're asking Order the serialization see this post.
https://stackoverflow.com/a/11309106/1181408
Update - Show that Order serialization works fine.
public class OrderedContractResolver : DefaultContractResolver
{
    protected override System.Collections.Generic.IList<JsonProperty> CreateProperties(System.Type type, MemberSerialization memberSerialization)
    {
        return base.CreateProperties(type, memberSerialization).OrderBy(p => p.PropertyName).ToList();
    }
}
public class JsonSerializationTest1
{
    public string Test1 { get; set; }
    public string MyTest2 { get; set; }
    public string Test2 { get; set; }
    public string Test10 { get; set; }
}
public class JsonSerializationTest2
{
    public string Test10 { get; set; }
    public string Test1 { get; set; }
    public string MyTest2 { get; set; }
    public string Test2 { get; set; }
}
[TestMethod]
    public void TestJsonOrder()
    {
        var test1 = new JsonSerializationTest1 { Test1 = "abc", MyTest2 = "efg", Test10 = "hij", Test2 = "zyx" };
        var test2 = new JsonSerializationTest2 { Test1 = "abc", Test10 = "hij", Test2 = "zyx", MyTest2 = "efg" };
        var test1Json = JsonConvert.SerializeObject(test1);
        var test2Json = JsonConvert.SerializeObject(test2);
        Assert.AreNotEqual(test1Json, test2Json);
        var settings = new JsonSerializerSettings()
        {
            ContractResolver = new OrderedContractResolver()
        };
        var json1 = JsonConvert.SerializeObject(test1, Formatting.Indented, settings);
        var json2 = JsonConvert.SerializeObject(test2, Formatting.Indented, settings);
        Assert.AreEqual(json1, json2);
    }