Why not measure it:
class Program
{
    class NameComparer : IComparer<string>
    {
        public int Compare(string x, string y)
        {
            return string.Compare(x, y, true);
        }
    }
    class Person
    {
        public Person(string id, string name)
        {
            Id = id;
            Name = name;
        }
        public string Id { get; set; }
        public string Name { get; set; }
    }
    static void Main()
    {
        List<Person> persons = new List<Person>();
        persons.Add(new Person("P005", "Janson"));
        persons.Add(new Person("P002", "Aravind"));
        persons.Add(new Person("P007", "Kazhal"));
        Sort(persons);
        OrderBy(persons);
        const int COUNT = 1000000;
        Stopwatch watch = Stopwatch.StartNew();
        for (int i = 0; i < COUNT; i++)
        {
            Sort(persons);
        }
        watch.Stop();
        Console.WriteLine("Sort: {0}ms", watch.ElapsedMilliseconds);
        watch = Stopwatch.StartNew();
        for (int i = 0; i < COUNT; i++)
        {
            OrderBy(persons);
        }
        watch.Stop();
        Console.WriteLine("OrderBy: {0}ms", watch.ElapsedMilliseconds);
    }
    static void Sort(List<Person> list)
    {
        list.Sort((p1, p2) => string.Compare(p1.Name, p2.Name, true));
    }
    static void OrderBy(List<Person> list)
    {
        var result = list.OrderBy(n => n.Name, new NameComparer()).ToArray();
    }
}
On my computer when compiled in Release mode this program prints:
Sort: 1162ms
OrderBy: 1269ms
UPDATE:
As suggested by @Stefan here are the results of sorting a big list fewer times:
List<Person> persons = new List<Person>();
for (int i = 0; i < 100000; i++)
{
    persons.Add(new Person("P" + i.ToString(), "Janson" + i.ToString()));
}
Sort(persons);
OrderBy(persons);
const int COUNT = 30;
Stopwatch watch = Stopwatch.StartNew();
for (int i = 0; i < COUNT; i++)
{
    Sort(persons);
}
watch.Stop();
Console.WriteLine("Sort: {0}ms", watch.ElapsedMilliseconds);
watch = Stopwatch.StartNew();
for (int i = 0; i < COUNT; i++)
{
    OrderBy(persons);
}
watch.Stop();
Console.WriteLine("OrderBy: {0}ms", watch.ElapsedMilliseconds);
Prints:
Sort: 8965ms
OrderBy: 8460ms
In this scenario it looks like OrderBy performs better.
UPDATE2:
And using random names:
List<Person> persons = new List<Person>();
for (int i = 0; i < 100000; i++)
{
    persons.Add(new Person("P" + i.ToString(), RandomString(5, true)));
}
Where:
private static Random randomSeed = new Random();
public static string RandomString(int size, bool lowerCase)
{
    var sb = new StringBuilder(size);
    int start = (lowerCase) ? 97 : 65;
    for (int i = 0; i < size; i++)
    {
        sb.Append((char)(26 * randomSeed.NextDouble() + start));
    }
    return sb.ToString();
}
Yields:
Sort: 8968ms
OrderBy: 8728ms
Still OrderBy is faster