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Due to their inability to self-regulate, ultrafaint dwarfs are sensitive to prescriptions in subgrid physics models that converge and regulate at higher masses. We use high-resolution cosmological simulations to compare the effect of bursty star formation histories (SFHs) on dwarf galaxy structure for two different subgrid supernova (SN) feedback models, superbubble and blastwave, in dwarf galaxies with stellar masses from 5000 < M _* / M _⊙ < 10 ^9 . We find that in the “MARVEL-ous Dwarfs” suite both feedback models produce cored galaxies and reproduce observed scaling relations for luminosity, mass, and size. Our sample accurately predicts the average stellar metallicity at higher masses, however low-mass dwarfs are metal poor relative to observed galaxies in the Local Group. We show that continuous bursty star formation and the resulting stellar feedback are able to create dark matter (DM) cores in the higher dwarf galaxy mass regime, while the majority of ultrafaint and classical dwarfs retain cuspy central DM density profiles. We find that the effective core formation peaks at M _* / M _halo ≃ 5 × 10 ^−3 for both feedback models. Both subgrid SN models yield bursty SFHs at higher masses; however, galaxies simulated with superbubble feedback reach maximum mean burstiness values at lower stellar mass fractions relative to blastwave feedback. As a result, core formation may be better predicted by stellar mass fraction than the burstiness of SFHs.