Perhaps I can contribute here, having owned a Note 1 for two years, my kids owning iPad mini's for a year and recently buying a Nexus 7. Obviously this is the original mini rather than the retina but the question of size is of relevance.
I originally bought a Note as I considered the (full size, not the mini) iPad to be too large for my needs. The Note had been fantastic over the years and nothing has come close to how useful it is. It has literally followed me
everywhere and is in my pocket even at home. If I could only have one device then it would be a smartphone like the Note. Smaller devices are just too limited for me now and I couldn't consider an iphone for this reason (my wife's iphone, while built incredibly well, seems a little toy like in size now).
Recently I've thought about replacing the Note with a Note 3 but instead of doing that I bought a 2013 Nexus 7 and plan to either keep the Note until it dies (it's close to that now!) or buy a midrange phone such as an SG3. The Nexus is fantastic. It has utterly exceeded my expectations. I considered another Mini but the Nexus' 32gb and a retina-like screen for £209 delivered to my door was simply too good to ignore. However I would still place the Mini above it marginally. I find my kids mini's a little frustrating to use compared to Android but that's probably because I am so used to it on my phone. However the form factor of the mini wins for me. It is simply a "nicer" aspect ratio with more on screen. That said, I can easily hold the Nexus 7 in one hand and type with the other - something I really don't think I could do with the mini.
So...
If you can only have one device then consider a Note.
If you like watching films, want something around £200-ish (£170 I think for the 16gb?), the flexibility of customisation or commute a lot and size is important then get something like the Nexus 7
If you mostly play games then the screen aspect ratio of the mini is best.
I'd say the mini is definitely the "better" device as it does what it's designed for incredibly well and Apple got the form factor spot on. The Nexus is great but still feels lacking something I can't quite put my finger on. However, if I were to buy again then I'd still have the Nexus 7 over the mini due to price and the fact I commute on a train every day so it is the better form factor for my own use case.
** I'm extremely drunk so please excuse any typo's