  ZF arose as an attempt to axiomatise the theory of wellfounded sets, and this principle is kept constantly in mind by the ZF-istes as they struggle to find new and more informative axioms. In contrast, the syntactic version of the noncircularity insight (which is the one that underlies NF) has been a much less fertile source of axioms for its offspring. Most new axioms for NF are either versions of AC or postulates of smooth behaviour by the \(T\) functions. It may be more natural to compare/contrast NF with Zermelo set theory rather than with ZF(C); Zermelo was a first attempt at formalising a theory of sets-of-ordinary-mathematics; it took a few decades for it to become clear that the pack of axioms needed the axiom scheme of replacement, and it could be argued that NF should be analogously augmented with axioms such as the axiom of counting (which says that the singleton function restricted to the natural numbers is a set), or with the axiom of choice for wellfounded sets.