I've had a Mini for 2 weeks along with my near year old iPad 3.
I spent a lot of time using both for direct comparison and found the following:
1. The resolution of the Mini only ever became an issue on large websites with a lot of complex formatting and tiny text (although my eyesight isnt the best)
2. The main complaint i have with the Minis screen is how inferior it is to its larger Retina counterparts at displaying complete RGB. It also has a distinctly less warm tone than the iPad 3.
3. Performance wise they ran identically on all apps tested.
4: Due to the massive weight difference i found myself forgetting i had hold of it in the way i would with my Kindle (a Paperwhite) this never happened with the iPad 3. After using a Mini for 10 minutes a full size iPad feels gargantuan.
5: If you use a Messenger bag (or any other manbag type thing) and travel around with an iPad everyday the Mini is much easier and takes up a lot less space.
6: Admittedly, i did find myself going back to the iPad 3 sometimes in the house. It is easier on the eyes.
7: The Mini wins for me hands down when it comes to gaming due to its size and weight, despite the already mentioned reservations with the screen.
8: Its much easier and quicker to charge the Mini. Charges in 3 hours rather than the 6 and a half with an iPad 3+10w charger. Unlike the 3 it can also charge from most USB ports.
9: The battery life is much better on the Mini. Getting on average 12 hours between charges
In the end i've decided to stick with the Mini and sell the 3. Although I don't think its fair to say either device is better, its defiantly a case of picking the one will suit your usage habits. Not everyone could justify having both a small and large iPad (i cant, at least not financially lol) but if you had money to burn i can see how people would could use both everyday. If you use your iPad a lot throughout the day, taking it with you everywhere or want to do some portable ios gaming i'd recommend at least looking at a Mini. However if you use it at home only the weight/size advantages do diminish significantly.