Analyses of Type Ia supernovae (SNe Ia) have found puzzling correlations between their standardized luminosities and host galaxy properties: SNe Ia in high-mass, passive hosts appear brighter than those in lower mass, star-forming hosts. We examine the host galaxies of SNe Ia in the Dark Energy Survey 3-yr spectroscopically confirmed cosmological sample, obtaining photometry in a series of local apertures centred on the SN, and for the global host galaxy. We study the differences in these host galaxy properties, such as stellar mass and rest-frame U R colours, and their correlations with SN Ia parameters including Hubble residuals. We find all Hubble residual steps to be <3 in significance, both for splitting at the traditional environmental property sample median and for the step of maximum significance. For stellar mass, we find a maximal local step of 0.0980.018mag; 0.03mag greater than the largest global stellar mass step in our sample (0.0700.017mag). When splitting at the sample median, differences between local and global U R steps are small, both 0.08mag, but are more significant than the global stellar mass step (0.0570.017mag). We split the data into sub-samples based on SN Ia light-curve parameters: stretch (x1) and colour (c), finding that redder objects (c < 0) have larger Hubble residual steps, for both stellar mass and U R, for both local and global measurements, of 0.14mag. Additionally, the bluer (star-forming) local environments host a more homogeneous SN Ia sample, with local U R rms scatter as low as 0.0840.017mag for blue (c > 0) SNe Ia in locally blue U R environments.