What do you mean by limited version on offer? Should be the latest version and latest supported underlying Python in every case. But it is not HASSIO indeed, which is an own operating system image, if this is what you mean, so the operating system config frontend is not available. There is a Docker container available I see, result might be something in the middle between Home Assistant Core and a native Home Assistent (HASSIO) system 
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Sorry I saw this now (or most probably saw it earlier and forgot to reply). What I meant was this:
https://www.home-assistant.io/installation/#compare-installation-methods
I ended up using a spare RPi3 as a dedicated Homeassistant server. Thanks for your support in any case 
yes we can install native HA Core only as the others are not really compatible with DietPi
For Supervised I did some testing in past. Theoretically it’s working but will break some DietPi functions. Especially network related https://dietpi.com/forum/t/home-assistant-supervised-on-dietpi/4726/8