Not much changed between the Raspbian Stretch images and the Raspbian Buster image from a user standpoint. All of the same content is available. There were updates to the system and it’s services with some minor user interface changes, but it’s still the same user experience. The main change was support for the Raspberry Pi 4 in Buster.
There is one bug within some versions of Buster that was causing Kiwix ( Wikipedia module support ) to not start every time and while I didn’t see it with the image I released, it was there at some point if Buster was updated from the terminal. It’s fixed now and there’s a note in the RACHEL-Pi downloads page on how to fix it if encountered, but it’s something to think about. In my opinion the Raspberry Pi4/Buster rollout has been anything but smooth and it would be good to wait until it’s more stable and with USB support before deployment. They have released some updates that have fixed the heat and other issues, but they’re still considered experimental. Once they’re stable and there’s a new image available at https://www.raspberrypi.org/downloads/raspbian/ I generally make new images.
KA-Lite hasn’t been updated in a long time while Kolibri is in active development. I would start with Kolibri as KA-Lite is considered a legacy project now. While you could run both at the same time, it’s better to choose one to save on system resources.
So I would say it’s between the Stretch or Buster Kolibri images and the choice is down to whether or not you use an SSD or USB with Stretch or an SD card with Buster. The two people with the most experience in deploying RACHEL-Pi that I’ve seen are @giakonda and @SHOMI. They’ve been kind enough to share that experience with other users so maybe they’ll answer any questions you have and can comment on stability. I know that @SHOMI has used SSDs with the stretch images.