I have both. Let me first say I am no fanboy. I hate fanboys. I go with what works. Right now Android works for me but if Apple or someone else for that matter comes out with something better, I am jumping ship.
I got the iPad Mini because of portability. Although I do have an iPad 2 and it worked great, it was not as portable as I liked it to be. If I am carrying it in my hand along with other stuff, I could easily see myself possibly dropping it. Not to mention, it became a hassle to carry. I ended up getting the iPad Mini so that I could have true portability. Hardware wise, it was very similar to the iPad 2. I really liked the size of the Mini as if felt comfortable in my hand and that I could hold it with one only. It is very light, it has a thin bezel and can handle almost anything you throw at it. The battery life was exceptional. The sound was okay . It also had the benefit of all the apps out there without a need for porting. I took this thing everywhere I went. I also loved there were so many choices out there as far as cases, mounting solutions and accessories. However, at one point, I wanted to start reading more and purchased a Kindle Fire HD. Mostly because of eBooks and ease of use although you could do the same with the Kindle for iPad. What I hated about the iPad Mini was that it did not have a nice display. The Kindle Fire HD had a much better display although it cost considerably less than the iPad Mini. The sound of the Kindle Fire HD was also superior (I am not a audiophile so others may disagree with me). Although I really loved the iPad Mini, there were a few things and customizations that I wanted to do that were just not available to me. It also never really felt like it was my own. In order to get any customization out of it, I needed to jailbreak it.
I then start reading about the Nexus 7. It was exactly what I wanted and best of all I could make it my own. Sure, some things were lacking like an equal number of apps as well as the quality of the camera and lack of ease of use with the Apple ecosystem. That however was not important enough for me to hold be back. I purchased the Nexus and fell in love with it. It is much snappier, has a better display, super customizable and very easy to root. It also has an awesome battery life and I can hold it even easier and more securely in one hand. Although there aren?t as many apps as the iPad, the apps can do so much. They truly allow you to make it your own. All the stuff that I wished iPad Apps could do can be done with Nexus 7. Occasionally I find myself using the Mini but mostly for nostalgia. Same as I do with the Kindle Fire HD. I just love the Nexus 7 much more than all the other tablets. You have Qi Wireless Charging, NFC Support, Great Hardware, perfect size. Anything the iPad Mini can do, it does it better (except for what I referenced above). Just wished they had more accessories, mounting solutions and variety from vendors the way the iPad Mini does.
My two cents. Sorry for the long response.