In the US, all schools that I know of charge tuition and fees. So there is no dichotomy of programs in this sense. Though some schools do not allow students to attend their doctoral program without having funding to pay that tuition/fees, either by a fellowship or from their advisor's grants, or perhaps via industry sponsor. I suspect this is because the faculty don't want to promise any time to advise students when they aren't getting funded for their own lab as part of the deal. The funding source, if there is one, then pays the tuition/fees. Beyond that, "self-funded" students are generally the same as those with fellowships; they can choose their project more freely and are not committing part of their time to being lowly research or teaching assistants. They may well have an industry job instead.
One drawback of course is a student is not a great judge of what is a good direction. Whereas the advisor's dogged pursuit of grants would tend to pull their own projects in the direction of more important problems which are probably better for the student's career. Choosing one's own direction also requires a patient advisor who is willing to continue advising while the student does run off and chases their own interests more freely.
At an opposite extreme is advisors who treat self- (or externally-) funded students the same as if the advisor was providing the funding anyway. I.e. they expect to set tasks and supervise the student, rather than simply advise them. Then you're paying out of pocket to be a research assistant. Which is certainly unfair.
As for whether there is some kind of ranking in the mind of hiring committees or firms down the road, regarding how you were funded, nope. A PhD is a PhD. It's primarily a hazing process anyway. The self-funded student will just be missing that line in the CV regarding your assistantship, which many do not put anyway since it is pre-doctoral.