The only change in the iPad Mini 3 from 2 is the addition of the fingerprint sensor. If this a device you're going to be hauling around with you on a daily basis that might be enough of a reason to go for the 3. If not, choose the 2 and save some money. The original iPad Mini is also available at a discounted price in the 16 GB only capacity. But I think the retina screen is a good reason to go with the Mini 2.
I'd also go larger than 16 GB. The recent update to iOS to 8 meant that many of us with 16 GB devices had to clear off most of our apps and data to be able to update the OS. I think 32 GB is the sweet spot which Apple has unfortunately phased out with this year's models. But it gives a good price comparison point.
Apple iPad Air 2 16 GB - $499
Apple iPad Air 16 GB - $399
Apple iPad Mini 3 16 GB - $399
Apple iPad Mini 2 (Retina) 16 GB - $299
Apple iPad Mini 16 GB - $249
Compare iPad models
NY Times Personal Tech: IPad Air 2 and Mini 3 Review: Fantastic, but Largely Unnecessary, Tablets
Android fansite picks iPad Air 2 as top tablet
I don't think there are any real standouts in the Android tablet market. Samsung continues to offer a dizzying array of options. But there are two distinct classes of tablets: the Galaxy Note focusing more on productivity and the Galaxy Tab which seems more recreational. Within the Note class is the higher end model the Galaxy Note Pro which is a 12 inch tablet touted as "Secure for enterprise with Samsung’s Knox solution." Galaxy Tabs come in a numbered version, currently 4, I believe and an S version. The S version seems about $150 more expensive than the numbered. Most come in a variety of sizes and capacities. The Notes come with the S pen which enables you to write on your tablet. There are lots of special deals for the holidays. I have no idea which one might be the right one for any individual. There is such a thing as too many choices.
Samsung Galaxy Tab Website - the manufacturer's website may be a good place to start if you want to try to figure out which model is best for you. They enable you to break it down by size, wifi vs. LTE. Then I'd probably look for online reviews of the model I'd selected. Some rate better than others.
For the Android purist, Google Nexus 9 is the latest Google branded device running the latest version of Android 5.0 Lollipop. While most tech journalists were quite enthused about earlier Nexus tablets, especially the Nexus 7, reviews of the Nexus 9 have been mixed. The primary reason to get a Google branded Nexus tablet or phone is that they don't come laden with the extra bloatware that manufacturers and carriers often put on Android devices. Neither do they have any customized User Interfaces. You get the device with the operating system as Google intended it. They also generally get updates sooner than devices from other sources so you're generally running the latest version of Android.
Google Nexus 9 from Google Play Store - 16 GB - $399
There are Android tablets made by other manufacturers. A quick check of BestBuy online shows that Samsung seems to really dominate this market. But you may find good tablets made by manufacturers such as Asus and Toshiba. They're worth considering. I'd probably look for some online reviews of the models you're considering. I think you do want to find something with a reasonably current version of Android on it. Android devices are a bit weak in the update department so you may very well be stuck with the version of the OS that you buy. If it's too old you may run into compatibility problems with current apps. As I said in the section on Nexus 9, the current version of Android is 5.0. The next most recent is 4.4. I'd try to stay close to that in any hardware I was buying today. My one caveat is to avoid the really cheap no name $100 tablets you might run into at Walgreen's or Shopko. These are often running really outdated versions of Android and may not even have access to the Google Play Store. This means you may not be able to do much with them at all.
I'll include Amazon Fire tablets here. They are running Android after all - a forked highly customized version of Android but they do fit the category. People seem to really like their Amazon Fire tablets. I think it's due to ease of use and generally low expectations. If you're looking for a tablet for someone who just wants a mobile device to surf the web, read and view Amazon content, and maybe play a few games, these tablets have decent hardware at reasonable prices. I think they could be a good value particularly the lower end models in the $99 - $179 price range. They're certainly a lot more useful than the no name tablets mentioned previously. But when you get to the higher end HDX 8.9 starting at $379, you're getting into the Apple iPad, Samsung Galaxy price range. Unless someone is a real Amazon devotee, the others offer a lot more options for apps, including Amazon.
Compare Fire Tablets on Amazon
A big subcategory of tablets this year seems to be tablets directed toward children. There are some manufacturers who specialize in this area notably LeapFrog and VTech. I can't say I know anything about either of those manufacturers. I'd probably do a little research if you're interested. But what struck me was the entry into this category by Samsung and Amazon Kindle.
This is the Samsung Galaxy Tab 3 Kids Edition - $199.99 list price
And the Amazon Fire HD Kids Edition - $189.99 list price
The nabi that I talked about in previous years is also back. But the nice thing about these kids tablets from major manufacturers is that you can no doubt share apps across devices. They're standard Android and/or Kindle Fire but with extra protection against drops.
The final entry into the tablet category are Windows tablets. 2-in-1s also fit into this category. Microsoft Surface Pro 3 is at the top of the line. Interestingly, Microsoft targets them in ads against Apple's Macbook Air tablet computer not against the iPad Air 2. And that's the price range you're looking at starting at $799 for a 64 GB model and goes all the way up to $1,949 for a 512 GB. These really are meant for people who want a touch screen laptop running Windows that can be taken apart and used as a tablet as well. There's certainly nothing wrong with that. It is a niche that will probably appeal to business users and those who want to do serious computing. But you're giving up the beautiful simplicity of iOS and/or Android in favor of a Windows computing experience.
There are a number of other manufacturers making Windows tablets and 2-in-1s among them Lenovo, HP, Toshiba, Acer, many of the computer laptop manufacturers with which you may be familiar. These are often cheaper than the Surface Pro 3. Once again, I'd look at online reviews if I were serious about purchasing a device in this category. And it never hurts to go to a store and try them out to see if you like the feel of a particular keyboard and test the weight.
My overall advice hasn't changed particularly from year to year. If you're buying a tablet for someone new to tablets, it's hard to go wrong with an iPad. Apple makes great hardware. The software and apps ranks highly for usability and availability. Since Apple makes its money off the hardware, they're pretty open to software and will run just about anything including Google and Amazon apps. If you're buying for someone who is already invested in the Android ecosystem, it's probably a good idea to stick with whatever s/he is most familiar with - Samsung, HTC, etc. If you're looking for a bargain for someone who is new to tablets and/or a heavy user of Amazon services, go with a Kindle Fire. They rank highly for usability but may prove frustrating to someone who wants to use Google or Apple services. Kindle Fire is pretty much limited to the Amazon App store and Amazon books, music and movies. It does run Netflix and Hulu Plus and some other streaming services.