Honestly, this is highly dependent on the specific code snippet. C++11 is only a newer revision of the C++ language standard (ISO/IEC 14882:2011).
A newer revision only changes the grammar of certain expressions and statements, and usage of certain keywords, as well as introducing new (and useful) stuffs, like rvalue reference (T&&), auto type deduction (auto and decltype), variadic template parameters (template <typename... Args>) and so on. In spite of the fact that some introductions may help you write more efficient codes (e.g. move semantics), it essentially does not change the way compilers are required to generate CPU instructions from C++ source codes.
So in micro-instruction level, the compiled instructions from the same source would mostly remain the same under C++98/0x/11, so there should not be any observable difference in performance.
What in fact matters the more is the algorithm you choose and the specific implementation you write, as well as compiler optimization (usually -O# command line argument). With new standards, you are allowed to write faster codes with move semantics, range-based for loop, decltype(auto) (this one is C++14, though)
In fact, this code generates exactly the same assembly code, when language standards is the only different option supplied to the compiler:
#include <iostream>
using std::cout;
using std::endl;
int main() {
cout << "Hello world" << endl;
return 0;
}
But when you start working with STL, which always use the latest features whenever possible, then it starts to make a difference:
#include <iostream>
#include <string>
using std::string;
string getString(void) {
string str("");
for (int i = 0; i < 100000; i ++)
str.append("A");
return str;
}
int main() {
std::cout << getString() << std::endl;
return 0;
}