||We present new neutral atomic carbon [C I] (3P1 → 3P0) mapping observations within the inner ∼7 kpc and ∼4 kpc of the disks of NGC 3627 and NGC 4321 at a spatial resolution of 190 pc and 270 pc, respectively, using the Atacama Large Millimeter/Submillimeter Array (ALMA) Atacama Compact Array (ACA). We combine these with the CO(2−1) data from PHANGS-ALMA, and literature [C I] and CO data for two other starburst and/or active galactic nucleus (AGN) galaxies (NGC 1808, NGC 7469) with the aim of studying: (a) the spatial distributions of C I and CO emission; (b) the observed line ratio RC I/CO = I[C I](1−0)/ICO(2−1) as a function of various galactic properties; and (c) the abundance ratio of [C I/CO]. We find excellent spatial correspondence between C I and CO emission and nearly uniform RC I/CO ∼ 0.1 across the majority of the star-forming disks of NGC 3627 and NGC 4321. However, RC I/CO strongly varies from ∼0.05 at the center of NGC 4321 to > 0.2 − 0.5 in NGC 1808’s starbursting center and NGC 7469’s center with an X-ray-luminous AGN. Meanwhile, RC I/CO does not obviously vary with ⟨U⟩, which is in line with predictions from photodissociation-dominated region (PDR) models. We also find a mildly decreasing RC I/CO value with an increasing metallicity over 0.7 − 0.85 Z⊙, which is consistent with the literature. Assuming various typical interstellar medium (ISM) conditions representing giant molecular clouds, active star-forming regions, and strong starbursting environments, we calculated the (non)local-thermodynamic-equilibrium radiative transfer and estimated the [C I/CO] abundance ratio to be ∼0.1 across the disks of NGC 3627 and NGC 4321, similar to previous large-scale findings in Galactic studies. However, this abundance ratio likely experiences a substantial increase, up to ∼1 and ≳1 − 5 in NGC 1808’s starburst and NGC 7469’s strong AGN environments, respectively. This result is in line with the expectations for cosmic-ray dominated region (CRDR) and X-ray dominated region (XDR) chemistry. Finally, we do not find robust evidence for a generally CO-dark-and-C I-bright gas in the disk areas we probed.