An extensive catalog of spatially-resolved galaxy rotation curves and multi-band optical light profiles for 1752 observed spiral galaxies is assembled to explore the drivers of diversity in galaxy structural parameters, rotation curve shapes, and stellar mass profiles. Similar data were extracted from the NIHAO galaxy simulations to identify any differences between observations and simulations. Several parameters, including the inner slope "S" of a rotation curve (RC), were tested for diversity. Two distinct populations are found in observed and simulated galaxies; (i) blue, low mass spirals with stellar mass M* < 10^9.3 Msol and roughly constant "S", and (ii) redder, more massive and more diverse spirals with rapidly increasing "S". In all cases, the value of "S" seems equally contributed by the baryonic and non-baryonic (dark) matter. Diversity is shown to increase mildly with mass. Numerical simulations reproduce well most baryon-dominated galaxy parameter distributions, such as the inner stellar mass profile slope and baryonic scaling relations, but they struggle to match the full diversity of observed galaxy rotation curves (through "S") and most dark-matter-dominated parameters. To reproduce observations, the error broadening of the simulation's intrinsic spread of RC metrics would have to be tripled. The differences in various projections of observed and simulated scaling relations may reflect limitations of current sub-grid physics models to fully capture the complex nature of galaxies. For instance, AGNs are shown to have a significant effect on the shapes of simulated RCs. The inclusion of AGN feedback brings simulated and observed inner RC shapes into closer agreement.