The diferences can be quite profound between a trainer and an advanced model, particularly a real warbird (as opposed to the 'stang trainer). It isn't just speed, it includes varying degrees of built-in instability, sudden violent responses to your mistakes, twitchy control responses & inability to recover from some departures from controlled flight. That is why trainers are the way they are & that is why students are strongly advised to start with a trainer.

There is another reason as well. If you are using the services & good graces of an instructor, your greatly protracted learning curve, plus the the very real stress that keeping you & your 'Stang, Corsair, etc, in one piece, is a great imposition on the instructor -- it can extend to abuse of his time and patience. There is probably going to be an incident where even a really good instructor won't be able to save you from a mistake (stalling at low altitude in final turn comes to mind) & your bird will be history -- & it won't be his fault, but he will almost certainly feel bad about it.

While it's your money, starting with a warbird or a hot sport plane will very greatly put your investment at risk, greatly extend your learning time & greatly impose on the instructor.