I have the 6s and not the 6s Plus, but I think of the iPad mini as a smaller iPad, not a bigger iPhone. If you do some math, the size difference between an iPad mini's screen and an iPad Air's screen is MUCH smaller than the difference between an iPad Air and an iPad Pro's screen.
I've been thinking a lot lately about whether or not I need both, and recently I have been doing some app/web page comparisons. To me, an iPad mini has a far different use case than the iPhone. The iPhone is my everyday general purpose computer. If I'm away from my desk or out and about, the iPhone/Apple Watch are my 1-2 punch for getting things taken care of. But if I'm going out somewhere and know I might have some down time to kill, the iPad comes with me every time. It's the perfect device for that. Games, reading, browsing, texting, email--I feel they're all more enjoyable on my iPad mini.
I've owned a lot of iPad models over the last few years, and I got a lot of hands on time with the Pro, but I still feel like the mini is my favorite iPad form factor. I'm more likely to take it out of the house with me because it's more portable and stowable than my iPad Air/3/2 were, and if I need to get more heavy lifting done, my 13" rMbp is not exactly hard to carry.