You do have a C++ tag, and you mention "declaring a string" in the question. Therefore there might be a performance difference (and yes, the printf could swamp it). Declaring a non-simple variable means calling a constructor, which might mean a non-trivial amount of work. In that case, declaring it inside of the loop could be hiding significant work in what appears to be an innocent declaration.
In general, the answer is that if you really care about performance - and treating the sample code as only an example of the difference between two places to declare a variable - then for non-simple variables, it is better to declare it outside the loop, unless the semantics require a fresh version of a temporary at each iteration.
There are likely many other places first to look at if performance is an issue, but one consideration is always moving loop invariants out of loops, especially if it is much easier for you to tell that it is invariant than for the compiler. And what looks like a declaration, can, in C++, fall into that category.
If, for (silly) example, you have
int k = 43;
for ( int i = 0; i < N; ++i )
{
int j = 17 + k; // k was previously defined outside the loop, but doesn't change in it
l = j * j; // l was also declared outside the loop
}
any good optimizing compiler can recognize that k is constant, and that j is always assigned 60, and l is assigned 3600 N times, and the loop can simply be removed and replaced with a single assignment to l. Here k and j are both loop invariants.
But a not-quite-so-good compiler might miss even one link in that chain, and wind up creating the loop.
It gets harder for the compiler to figure things out when you have
Foo k( 43 ); // a class that takes an int argument to its constructor
for( int i = 0; i < N; ++i )
{
Bar j( k ); // a Bar takes an int argument, adds 17 and stores it.
l = j.squared();
}
Same invariants. Not as easy to detect without looking inside the workings of bar; and if the constructor and squared method aren't inline, we've just made it slower.