simplexml_load_string() (as the name suggest) load xml from a string and returns an object of SimepleXMLElement. There is no difference between this and using just the usual constructor of the class.
Update:
SimpleXML::__construct() has an additional parameter (the third one) bool $data_is_url = false. If this is true the behavior is the same as simplexml_load_file() (in conjunction with the common stream wrappers). Thus both simplexml_load_*()-functions cover the same functionality as SimpleXML::__construct().
Additional the functions simplexml_load_*() has a second parameter string $class_name = "SimpleXMLElement" to specify the class of the object to get returned. Thats not a specific feature of the functions, because you can "use" something very similar with usual instanciation too
class MyXML extends SimpleXMLElement {}
$a = new MyXML($xml);
$b = simplexml_load_string($xml, 'MyXML');
A difference between the OOP- and the procedural approach is, that the functions return false on error, but the constructor throws an Exception.