Can you be more specific? I don't see it that way at all. I've "rented hardware" and provisioned AWS machines, and the broad experience is basically identical. There are "APIs" on both sides that do pretty much the same thing (though with the smaller hosting providers that API is often "call them on the phone" -- not an advantage, IMHO).

The differences are in scale (how many can you get and how fast -- cloud wins huge here), price (cloud hosting is more expensive over the long term) and granularity (bill by the hour vs. by the month).