I'll chime in, just my 2 cents...
Being on the road a lot for business this past month, I bought a Kindle Fire HD 7" to keep myself occupied. I had originally gone in to get the Kindle Paperwhite but Best Buy wasn't stocking them yet and, as the KFHD was only $80 more at $199, I thought, why not. It wasn't bad. I felt like it was a little heavy but, after checking the specs of the iPad Mini, I see that it's only 85 grams heavier.
I downloaded Netflix and HBOGO apps and side-loaded some episodes of The League onto it to watch while bored at night at the hotel. I read books that I had read on my old Kindle (given to my mom) but didn't really like the bright LED screen. I bought one or two apps (Angry Birds Space) but wouldn't go any farther than that because I already had bought a decent amount of game apps for my iPhone which are universal. I didn't feel like buying a bunch of apps for a whole new OS.
The main thing that attracted me was the price. At $199, it's almost an "easy" purchase. At the time I bought the KFHD, iPad Mini rumors were starting to firm up. I wanted one but, at the rumored price point (now shown to be true), I was turned off. Now that it's been announced I'm just as turned off. It's $130 more (almost twice as much) than the Kindle Fire HD. Is the iPad Mini a better product? Probably. Does it do anything different? I really don't think so. It may do some (most) things better. Yes, all of my iPhone/Universal apps will work on an iPad Mini. Sure, I can not play all the games I don't play on my iPhone on the iPad Mini.
I guess, now that I'm back at home more often instead of on the road, I wonder if I really need either. I ended up returning the Kindle Fire HD after about 3 weeks because, to be honest, it was laggy, it was a chore to use it to surf the internet and, I didn't feel like investing in a bunch of Android time-waster apps that I already have on my iPhone and don't use enough as it is. Also, being so used to iOS, I felt like trying to do anything on it just wasn't as easy as it should be, like the majority of stuff on the iPhone is.
I may end up getting either an iPad 2 or an iPad Mini simply for the fact that, as an architect, I've always wanted to create a portfolio I could load onto it that would be interactive. Also, it's a great presentation tool. My boss and a few coworkers use them. Also, I didn't see any "iMovie" or "iPhoto" apps for the Kindle and I think I would use those.
The Kindle Fire HD is not a terrible product and, for someone that already has an older Kindle (even if they also have an iPhone), it's an easy upgrade.