AFAIK ArrayCtrl Sort() uses Value comparison that in case of Strings uses DefaultLanguageCompare() function in LangInfo.cpp. However String comparison uses String0::Compare() in AString.hpp.
If you prefer the second, I suppose that you have to create a comparison function like this;
int MyStringCompare(const Value& a, const Value& b) {
return a.ToString() < b.ToString();
}