is_a is a function, whereas
instanceof is a language construct.
is_a will be significantly slower (since it has all the overhead of executing a function call), but the overall execution time is minimal in either method.
It's no longer deprecated as of 5.3, so there's no worry there.
There is one difference however.
is_a being a function takes an object as parameter 1, and a string (variable, constant, or literal) as parameter 2. So:
is_a($object, $string); // <- Only way to call it
instanceof takes an object as parameter 1, and can take a class name (variable), object instance (variable), or class identifier (class name written without quotes) as parameter 2.
$object instanceof $string; // <- string class name $object instanceof $otherObject; // <- object instance $object instanceof ClassName; // <- identifier for the class