In the first example, this:
.then(stdout.write)
is equivalent to this:
.then((String sText) {
stdout.write(sText);
})
Technically there's one more function call, and you have one more variable, which should cost you a few bytes (I'm not sure on the exact implementation). Strings are immutable; you are only receiving a reference to the String, so you are not saving resources (other than the function call and a few bytes of memory) by using second version.
Whatever it is you want to do with the contents of the String probably will involve using resources, of course, but that shouldn't be an issue unless the file is huge.