My wife got a mini for Christmas, I got a nexus 7 and already had a iPad 4 so I'm in a good position to comment!
Firstly I've read allot about the supposedly poor screen of the mini, this is simply untrue the screen quality is great and far better than the nexus 7 and really not that much worse than a retina iPad.
Screen Size, I feel the mini might be the perfect size, browsing is just as comfortable on the mini as on the iPad 4 and if if the specs get bumped up to its bigger brothers then I'll be switching next upgrade. However for true portability the Nexus 7 wins here, I can literally fit the nexus in a pocket.
Physical size, To look at all three devices side by side I would say there's a bigger difference between the mini and nexus than there is between the mini and iPad 4. Because of the size and cost of iPads I'd say they aren't truly portable take anywhere devices and this is why I bought a nexus as well!
My wife is over the moon with her mini and if I'm a honest I'm a little disappointed with the screen quality of the nexus after being spoilt by a iPad 4 and Galaxy S3, it's no where near as good as the mini's either. But at least it fits in my pocket, offers allot of power and I won't worry as much if I lose or break it!