It's not that hard to do the math. Go to each carrier's web site, look at their plans, the cost of a new iPhone with plan and then compare that to whatever per-pay company or plan you were thinking of. Carriers put their plan fees and everything you need to know to compare right there on their web site. But withou knowing specifically which carrier, which plan(s) (do you want or need unlimited everything? Do you want or need tethering?) it is impossible to give a simple answer to your question.
Do you bundle any other services with your cell phone carrier (land lines? Internet? television?). That can also have an effect on your bottom line out of pocket fees.
Also keep in mind that for most per-pay plans with a smart phone in the USA, you will be actually getting service from an MVNO, not the actual company that owns and runs the network. That may or may not matter to you, but it is a factor in many people's decision as well.
IMO, there is no single nor simple answer to your question - too many variables left unaswered by your question to make for a single answer.
