One not so big advantage for the older delegate
syntax is that you need not specify the parameters if you dont use it in the method body. From msdn
There is one case in which an anonymous method provides functionality
not found in lambda expressions. Anonymous methods enable you to omit
the parameter list. This means that an anonymous method can be
converted to delegates with a variety of signatures. This is not
possible with lambda expressions.
For example you can do:
Action<int> a = delegate { }; //takes 1 argument, but not specified on the RHS
While this fails:
Action<int> a = => { }; //omitted parameter, doesnt compile.
This technique mostly comes handy when writing event-handlers, like:
button.onClicked += delegate { Console.WriteLine("clicked"); };
This is not a strong advantage. It's better to adopt the newer syntax always imho.