I'm not sure it's worth to discuss this issue. To ensure consistency within the code base the preferred data types should be noted in the wiki. I know this can be a sensitive and subjective issue...
Only use BCL data types

String text;
String.IsNullOrEmpty(text);
Double number;
Double.TryParse(text, out number);

Only use language data types

string text;
string.IsNullOrEmpty(text);
double number;
double.TryParse(text, out number);

Use language data types for declarations | BCL data types for calling members

string text;
String.IsNullOrEmpty(text);
double number;
Double.TryParse(text, out number);

My favorit is the last option because

• an Enum can't inherit from UInt32 so you have to use uint
• because it's not obvious that data types have members
• MSDN says "√ DO use a generic CLR type name, rather than a language-specific name, in the rare cases when an identifier has no semantic meaning beyond its type."