If you install Supervised, you get the ability to run other software at an OS level, this can’t be done with the image based install. If everything you may want to install can be install via an add-on using HA OS image based install, then do that as it’s fully supported and made to be easy
Raspberry Pi OS.
You will need to keep your system up to date yourself, and won’t be able to ask for official support on Github. Community support only.
Follow this for Supervised on a Pi. Just substitute any reference of raspberrypi3 for rapsberrypi4.