The similarities between DJI's and Yuneec's consumer quadcopters are many. Both have 4K cameras with stabilizing gimbals. Both are "ready to fly," which mostly means there's no assembly required; just charge and go. Both are easy for beginners to control, and both offer first-person view (aka FPV), or the ability to see what the camera is seeing in the air in real time, usually via the transmitter/controller. There are other products that offer a similar feature set, but DJI and Yuneec have done a good job packaging them in ways that appeal to new flyers and hobbyists alike.
There are also some significant differences and on paper, at least, many of them are in Yuneec's favor. Despite being slightly more expensive, the Typhoon offers better value. The $1,299 4K version is available with a carry case (you'll need to buy one for your Phantom). It also comes with two batteries versus one on the Phantom. Then there's the transmitter, which has a built-in touchscreen display. This is how you view what the Typhoon's camera sees (you can also use it to access settings). In contrast, DJI users need a phone to do this, this approach works well, but is one more thing to bring along/charge. The last, and perhaps coolest extra with the Typhoon, is the Steadygrip, a hand-held mount for the 4K camera. Detach it from the drone, clip it to the accessory and you can film smooth video on the ground, too. DJI's working on a similar product, but it's not available yet, and won't ever be in the box of the Phantom 3 (the camera is non-removable).
You're also getting more flight features with the Typhoon. The ground station has GPS in it (actually, most quadcopters do, but not always the transmitter). This means the Typhoon has options like "follow me" and "watch me," which Phantom 3 doesn't have right now (but some features are coming eventually). So, the Yuneec is the one to get, right? Maybe. The real test is taking it up in the air and shooting some video. Which is, of course, what I did.
I'll preface my impressions by stating that I learned to fly on a Phantom, and have flown one for many hours, so this is what I am used to. Yuneec made the Typhoon pretty easy to fly. I had a few minor wobbles the first time, but this might be because of my prior Phantom experience. One example is that, by default, the Typhoon won't fly within 26 feet of you (or, really, the transmitter).
This caught me off guard when I first tried to land, as I'm used to bringing the Phantom in real close, and sometimes "catch landing" (getting it low enough to hold the landing gear, and make it think it's on the ground). I had the Typhoon above water, and it wouldn't come nearer. I had to walk backward far enough to be able to land it on solid ground, and not in an ideal spot (see the photo at the top of this article). The same problem can catch you out mid-flight, too. It'll suddenly stop moving as it hits the exclusion zone around you. I get it; it's a safety feature (and one you can turn off).
The Typhoon's biggest problem in the air, I found, was that it's not as responsive as the Phantom. DJI's consumer product is quite a bit smaller, and responds quickly to any touch on the controls. You can throw it left to right quite sharply, and it'll visibly pitch (but hold its position), and it manages to do so while keeping the camera steady -- though if you really throw it, the landing gear/propellers can get in the shot. The Typhoon felt more sedate. Not sluggish, but less immediate. You can control its speed, but that doesn't change the general responsiveness. Some might say this is a benefit, since I only once got propellers in the shot. But I do prefer the tighter feel of DJI's setup.
What the Typhoon does have going for it is excellent battery life, so you get more time in the air. On average I got 20 minutes before it would start warning me to bring it home. The Phantom 3 starts complaining between 15 and 17 minutes, I've found. It might not seem like a big difference, but those extra few minutes feel like hours when you're behind the sticks. One minor thing: I've never been a fan of how the Phantom 3 looks, but I like the Typhoon even less. As one colleague put it, it looks like it should fire Nerf bullets. It's a little... on the boyish side. The Phantom 3 isn't handsome, but smaller and more unthreatening.