Anytime a heartless is created it also creates a correpsonding nobodies. You have the stong heart part confused. Those that have stong hearts retain their form, but with the faintest visible changes Like Xehanort who took the name of Ansem when his heartless was created it Kept it's form and the Nobody Xemnas also was similar looking.
No, they don't have it confused... I specifically remember Yen Sid saying that when a person with a strong will becomes a Heartless, the body becomes a Nobody... but the ones with the most powerful wilsl (or it could be hearts, since willpower is probably linked to the heart) the Nobody maintains their human form with slight (although "slight" could be taken different ways) changes. This serves as a contrast to the fact that the most powerful types of Heartless (with the exception of Xehanort's Heartless, but we don't know why he retained his human form) are more and more monstrous. A strong heart can't be the key to retaining human form while a Heartless, because otherwise Sora would have kept his human form when he temporarily became a Heartless instead of turning into a shadow.
As for who would win... excluding the Organization, taking into account the vast number of Heartless as opposed to the Nobodies, the different powerful varieties of Heartless, and the fact that not counting the Organization there's only one boss Nobody (Twilight Thorn), the Heartless win hands down... though the Nobodies are stronger.