That is, if I'm coding something entirely in PHP4? Or perhaps I should use a custom function or class/extension instead to count the number of characters in a multibyte string?
Only difference I can spot is that mb_string strips out bad sequences, while iconv_strlen doesn't.
If you want a drop-in replacement for plain strlen, use mb_strlen as it always returns an int. This is very debatable though (iconv's correctness over mb's tolerance), but in practice mb_strlen's fault tolerance served me better. Just make sure you configure mb to the desired encoding either in php.ini or in a central place in your application.
Unicode support in PHP is in a bad place, you have to be aware of many pitfalls and exceptions. Having done a complete switch of several large applications and their user data to UTF-8, I could cry you a river.