I can give my feedback, I don't own either but our work got an ipad Mini in yesterday (and I spent 20 mins with it), and my friend has a Nexus 7 which i've used. So i can give a hands on response albeit i haven't used either with longevity:
in a straight out which is better i'd say the iPad Mini, and in all honesty it's not even close. It's thinner, prettier, has a larger display and is lighter. The main thing being used to attack the iPad mini is its 'no retina display'. On yesterdays use i actually think thats a damp squib. It's still very clear, and games look great on it. Two negative notes though, the camera is meant to be 5MP. The results i got from my 3 test pics looked more like something from a 2MP camera. Also it seemed to gather loads of fingerprints for a supposed anti-fingerprint screen. Web browsing seems smoother on the mini, and the lack of retina isn't a problem when reading small print.
But the real crux is it worth the huge price hike over the Nexus 7 (which is extremely good value). Unfortunately i need to give a big shoulder shrug as i think it will depend on the person, how much they're willing to spend. Nexus 7 is a lot more flexible in its customisation and tinkering. My friend uploaded emulators with ease to his Nexus 7, which perform really well. It beats the Mini hands down if you're a bit more of an advanced user and more into that sort of thing. Although I find the Nexus 7 is dissapointingly heavy in proportion to its size.
So yeah the good news is if you buy either you're a winner as they're both great. I think Mini wins on quality, Nexus 7 on value.
The main weakness of the Mini as I see it is not in it as a piece of hardware but it's where it's been positioned in the market I think. The 16GB model is £270, if they brought it in at about £240 it would be a more justifiable purchase. It's a great product, but the decision to break the psychological £250 barrier is a pity.