Honestly, as an Apple fanboy, I would say the only benefit of the iPad over the other two is the app library. The iPad mini is severely overpriced for the hardware that is in it. Also, I would only ever recommend buying an iDevice if you are comfortable jailbreaking it as Apple is quite restrictive on features because they want to control everything for quality control sake. Even then I would recommend staying away from the mini as it just seems like a terrible value to me (If it had a "retina" display that might be different). The Android tablets offer much more flexibility and power.
I personally would go for the Nexus 7 as it doesn't come with any front-end software and is the stock version of Android, but that's just a personal taste — many people love the various front ends different companies add to Android.
In terms of the amount of "apps" available for the iPad over the other two, it's more than double, but there are a ton of Android apps that do everything any iOS app can. Many of the iOS apps are just copies of other iOS apps.
All in-all it depends on what you want to do with it. the iPad will have the greatest selection of games and most game developers go for iOS before Android, just because it's the more popular platform. There are plenty of great games for Android devices, but for gaming, the iPad is the way to go because of the vastly greater array of options. Productivity apps should be comparable between the two operating systems and of little concern.
It used to be the case that because iOS devices were so efficient, they were much more responsive than the Android devices, but now Android devices have become so powerful, you won't notice. Go to a Best Buy if you can and play with each one and see what feels the best to use. See if you can notice any input lag, etc.
All-in-all, I personally do not think iPad mini is worth it's asking price.