Tablet design by its very nature is defined first and foremost by the screen and here the two tablets seem fundamentally different. Apple sticks to the original 9.7" screen of 4:3 aspect ratio, while Samsung uses the common 16:10 10.1" screen format.
Surprisingly, the two tablets are aren't that different in size - the Apple iPad Air measures 240 x 169.5 x 7.5, while the Samsung Galaxy Note 10.1 2014 is a bit bigger on the sides, 243.1 x 171.4 x 7.9 mm. Thin, iPad mini-like bezels is what allowed Apple to make the square-ish screen fit into the body of a widescreen tablet.
The difference in screens is nonetheless profound, and it will be properly covered in the next chapter.
Screens aside, the two tablets differ in something as simple as orientation - the button and front-facing camera placement of the iPad Air favor portrait usage, while those of the Galaxy Note 10.1 2014 lean towards landscape. Obviously you can use both tablets either way, but you'll find yourself sticking to the manufacturer-suggested orientation most of the time.
To be honest, we prefer on-screen buttons on tablets as they offer more flexibility and rotate with the rest of the screen.
Anyway, the wide-screen Galaxy Note 10.1 2014 shows its multimedia nature with two loudspeakers positioned on the left and right side of the tablet. This creates a a more immersive audio experience than the stereo speakers on the iPad Air, which are both located at the bottom (or rather on the side as you'll be watching videos in landscape orientation). The Samsung tablet also pulls ahead with audio enhancements from SoundAlive and Adapt Sound technologies.
The multimedia aspect is also seen in the addition of a microSD card slot. Sure, you can get a 128GB iPad Air, while the Galaxy Note 10.1 2014 tops out at 64GB of built-in storage, but let's be honest- a 128GB Air costs an insane amount of money. 64GB microSD cards are around $50 a pop, so a 16GB Note 10.1 2014 is still an option for heavy multimedia consumers. A cheap option at that, Apple charges a $100 premium every time the built-in storage doubles.
The front-facing camera on the iPad Air is in the middle of one of its short sides, similar to the placement on the iPhone. This is good for one-on-one video chatting and selfies. The camera on the Galaxy Note 10.1 2014 is positioned near the middle of one of its long sides, which fits the widescreen better with multiple people involved.
And while you're holding the Note 10.1 2014 horizontally, you'll notice the IR blaster at the top. It can control home equipment like TVs, disc players and set top boxes, placing it in charge of your home theater setup. At the very least, you have the option to change the channel if you're on the tablet while the TV runs in the background, a scenario that is probably well familiar to most users.
On the connectivity side, Apple uses the proprietary Lightning adapter, which can be plugged in regardless of the orientation. However, microUSB cables are far more common than Lightning cables, which you'll feel instantly if you need to borrow a cable. They are also much cheaper if you need to get a second one for the office.
The iPad Air connector boasts TV Out functionality, though you'd need an adapter. Still, it's a great option to have - either for watching movies or for doing presentations. The upside of the Note 10.1 2014's microUSB port is that you can plug in peripherals like external storage, keyboards and mice if you get a USB OTG cable (those are quite cheap and easy to find). With the proper adapter you can get HDMI out too.
Speaking of connectivity, both tablets come in either Wi-Fi only or 4G LTE versions. The Apple iPad Air has only one 4G LTE version, which covers 3G UMTS, CDMA and 4G LTE. The Samsung Galaxy Note 10.1 2014 comes in 3G (powered by a Samsung Exynos chipset) and 4G (powered by Snapdragon 800). Note that the 4G LTE on the Samsung is Cat. 4, which offers downlink speeds of up to 150Mbsp, over the Cat. 3 of the iPad, which tops out at 100Mbps. But neither Note 10.1 2014 version has CDMA connectivity, which limits the choice of carriers for North American users.
Apple's iPads have always had aluminum unibodies, but the one on the iPad Air is the best yet, by far. It's the slimmest too (iPad 3 and 4 were thicker than 2, Air is thinner than 2) and noticeably lighter. The thinner side bezels help a great deal in handling the tablet, but it's still a two-hand device. Then again, so is the Note 10.1 2014. Anyway, the aluminum design of the iPad Air is attractive and isn't out of place anywhere.
Samsung's designs are best known for their glossy plastic but the 2014 edition of the Galaxy Note 10.1 2014, just like the Galaxy Note 3, has a faux-leather back. It feels reasonably close to leather to the touch and looks pretty attractive. Less subjectively, the textured plastic feels warmer and offers more grip than the naked metal of the iPad.
Winner: Samsung Galaxy Note 10.1 2014. It was close, but the Note 10.1 2014 is more flexible in terms of storage, has better connectivity (unless you're a Verizon or Sprint user), including an IR blaster.
Some will prefer the metal looks of the Apple iPad Air and maybe value wired TV-Out over cheap storage. North American users also have to consider the CDMA support, unless they're looking for a Wi-Fi tablet.