Try the following
typeField == typeof(string)
typeField == typeof(DateTime)
The typeof operator in C# will give you a Type object for the named type. Type instances are comparable with the == operator so this is a good method for comparing them.
Note: If I remember correctly, there are some cases where this breaks down when the types involved are COM interfaces which are embedded into assemblies (via NoPIA). Doesn’t sound like this is the case here.