I've been an iPad user for a long time. 
In the past, I've written here about how I use my iPad to be more productive with a Zagg keyboard and Evernote. I've had the original iPad, the iPad 2, and the iPad 3; the the iPad 3 is the main basis for my comparison here.
A few weeks a go, I received my iPad Mini (it took a couple of weeks for Apple to ship it - well worth the wait) and have been using it regularly long enough to share my experiences.
By the way, I have the iPad Mini with AT&T LTE broadband, and 64GB of memory - I went with the larger memory because I download a lot of movies to watch on business trips, and they take a lot of room. I chose the broadband because I am often in high-security buildings where I cannot get on WiFi and I need another option.
Summary of my experience
Size
I wasn't sure what to expect from the iPad Mini, but I must say that I was very surprised at how much smaller, lighter and thinner it feels when you carry it. It is comparable in size and weight to my Kindle Touch e-Reader, which means I don't have to think twice about whether to bring it with me or not (I sometimes left my iPad 3 at home on long trips to save weight and/or free up space in my laptop bag.
Not only does the iPad Mini fit well in my laptop bag, it is small enough to fit in the pocket of my jacket - I love that. Since I use the iPad for so much of my note taking, list making, etc. for my productivity habits, it is a huge benefit when I can take a device almost anywhere.
Screen and on-screen keyboard
The screen has a much lower resolution than my iPad 3, but the lower resolution works well due to the smaller dimensions of the iPad Mini. The screen is plenty bright when you turn it up, and I end up turning it down pretty far for normal use (which also saves battery life).
I didn't have trouble using apps normally, and haven't yet found any apps that don't adjust correctly to the iPad Mini screen.
One thing that required adjustment: The on-screen keyboard. in Landscape mode, the screen is now too narrow for me to try to mimic touch-typing (I have big hands) but in Portrait mode, I can now thumb-type very well. As a side effect, for quick notes using the on-screen keyboard, I rotate it to portrait mode and jot things down in email or Evernote.
After a week or so of thumb-typing I ended up ordering Zagg's keyboard case for the iPad Mini, (right) as well. This is the little brother of the keyboard I reviewed previously. Zagg makes a 7-inch keyboard case that is the same width as the iPad Mini, but I went for the slightly larger 9-inch keyboard because I have larger hands. Even the 9-inch version is plenty small to pack or carry, and I have been very glad that I bought the Zagg keyboard.
Battery life
In spite of its much smaller size, the battery life is comparable to my larger iPad and meets the claimed 10-hour battery life Apple claims. This means I can use it to take notes and check email all day, I can watch movies on flights, and I can look things up online without having to worry much about when I'll be near a power outlet.
Miscellaneous
- I have the Apple Smart Cover for the iPad Mini but I don't like it nearly as much as I like the Smart Cover for the iPad3. The smaller size isn't as stable when using the cover as a stand, and the new magnet mechanism doesn't hold on as firmly as on the larger iPads (Apple covered the magnets in rubber rather than leaving them exposed, which I think leads to a weaker connection). Therefore, I rarely use the Smart Cover, and tend to use the Zagg case most of the time.
- The iPad Mini is another one of those devices that uses the new Lightning connector. This is fine for me, since I already have an iPhone 5 and had to go through the pain of getting extra cables and adapters for my old docks and accessories to work with the new connector. If you already have a sprawling ecosystem of chargers, cables, and docks from your older iPad, factor this into the transition process.
- I highly recommend getting a short adapter to convert your older, 30-pin connections to Lightning. I prefer the kind with the short cable rather than the all-in-one adapter that is a solid block of plastic - I find the short length of cable makes it far more useful.
Net-net:
Pros of the iPad Mini:
- The size is perfect for everyday use, and much more practical than my larger iPad.
- The battery life is great.
- Cameras (front an rear) are very good (and you don't look quite so foolish taking a picture with this one, like you do with the larger iPad.
- Screen is bright and very usable for email, reading, note taking, movies, and games.
- Huge ecosystem of existing apps works great with the iPad mini.
Cons of the iPad Mini:
- On-screen keyboard is not great for extensive text entry.
- Smart Cover not as useful as on the larger iPads.
- Accessory ecosystem still limited (but this will improve once this device has been around longer).
- Pricey.
The bottom line? I really like the iPad Mini. If I were buying today, or I could only have one iPad, I'd choose the iPad Mini.