I have an iPad Air and we share a 'family' iPad mini. I've used it occasionally, but really can't see why someone would have both. They both do the same, run the same software (apart from split screen on iOS 9, but I'm basing this off an iPad Air vs iPad mini 2) just are slightly different sizes.
For what it's worth, I much preferred the Air as I mainly use it for web browsing, Netflix and reading and prefer the bigger screen.
I have both and use both. The Air is ideal for home use, but I find it a bit to big to carry around away from home. The mini fits that bill perfectly.
Both have plastic rear covers, smart front covers, and tempered glass screen protectors fitted, and for me at least, are ideal.
They are an Air 32gb, and a Mini 2 32gb, both wi-fi only.
I have an iPad air 1 waiting in its box for my next school year, we have a family iPad mini that only my mum uses now.
I don't really use tablets, I use my laptop (Windows and Linux) for my main computing and my phone (Android) as a backup.