Resharper recommends changing CompareTo to CompareOrdinal

I have a sorter which performs various comparisons. Resharper says I should change from String.CompareTo to String.CompareOrdinal. Does this really provide much benefit or is it something I should adjust the inspection rules for?

CompareTo:

config.Sort(delegate(configData data1, configData data2)
{
    if (data1.SettingName.Equals(data2.SettingName))
    {
        string m1 = data1.SettingMachine;
        string m2 = data2.SettingMachine;
        if (m1 == null)
            m1 = string.Empty;
        if (m2 == null)
            m2 = string.Empty;
        return m1.CompareTo(m2);
    }

    return data1.SettingName.CompareTo(data2.SettingName);
});

CompareOrdinal:

config.Sort(delegate(configData data1, configData data2)
{
    if (data1.SettingName.Equals(data2.SettingName))
    {
        string m1 = data1.SettingMachine;
        string m2 = data2.SettingMachine;
        if (m1 == null)
            m1 = string.Empty;
        if (m2 == null)
            m2 = string.Empty;
        return String.CompareOrdinal(m1, m2); ;
    }

    return String.CompareOrdinal(data1.SettingName, data2.SettingName);
});