Update
As of PHP 5.3.9, the functionality of is_a() has changed. The original answer below states that is_a() must accept an Object as the first argument, but PHP versions >= 5.3.9 now accept an optional third boolean argument $allow_string (defaults to false) to allow comparisons of string class names instead:
class MyBaseClass {}
class MyExtendingClass extends MyBaseClass {}
// Original behavior, evaluates to false.
is_a(MyExtendingClass::class, MyBaseClass::class);
// New behavior, evaluates to true.
is_a(MyExtendingClass::class, MyBaseClass::class, true);
The key difference in the new behavior between instanceof and is_a() is that instanceof will always check that the target is an instantiated object of the specified class (including extending classes), whereas is_a() only requires that the object be instantiated when the $allow_string argument is set to the default value of false.
Original
Actually, is_a is a function, whereas instanceof is a language construct. is_a will be significantly slower (since it has all the overhead of executing a function call), but the overall execution time is minimal in either method.
It’s no longer deprecated as of 5.3, so there’s no worry there.
There is one difference however. is_a being a function takes an object as parameter 1, and a string (variable, constant, or literal) as parameter 2. So:
is_a($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