If you have a better intuitive feel for one equivalent over another, that is a perfectly valid reason to prefer to trade it. The last thing you want to do is make the wrong adjustment because of some mental hiccup while dealing with a new type of position.
Thank you, Commiebat. One of the main benefits for me using the covered put write is that I only have to watch the stock price, not the option. Only the stock can hurt me, not the option.
Is also possible to write puts, covered, against LEAPS see : http://www.advfn.com/p.php?pid=fbb_thread&id=754447&bb_id=5