A bit of heresy from me here I'm afraid!
In our house daughter has an Ipad mini, husband has a Nexus 7 and I have a Kindle Fire HD.
The Ipad mini seems to have become surgically attached to daughter's hand so I haven't had much chance to play myself. She's basically using it as a big Ipod Touch and it seems very nice, but probably not worth the extra cost apart from the fact that it fits in with her existing set up.
The Nexus 7 is very nice, but husband is a bit of a technophobe and doesn't seem to find it easy to work out how to do stuff. Consequently I've had plenty of opportunity to work out how to download apps, upload music etc. He doesn't really use Google services much and I think that he might have found the Kindle Fire HD a bit easier to cope with.
I am not a technophobe and am fairly ok with computer stuff. I'm finding the Kindle Fire HD very intuitive to use and haven't found any difficulty finding apps to do what I want from the Kindle apps store. I did follow some instructions on the Kindle discussions board to get Dolphin browser and flash for ics. A snow clearing app would come in quite handy atm as it's snowing hard again and I have to try to get the car out shortly!
The Kindle Fire HD is slightly wider than the Nexus 7, I think that makes it look better. Its speakers are much better than the Nexus's and I can use it to watch Lovefilm on the TV using the hdmi out slot.
So, a vote for the Kindle Fire HD from me.