That is good question and they are relatively similar drones in terms of features and price. If it was a few months earlier I would say the Yuneec 4K would be better in terms of features, but a few months back DJI released some new flight features for the phantom which enabled them both to perform cool flight features such as follow me, and circle point etc.. So now one can argue that the Phantom 3 actually has more flight modes than the Yuneec Q500. However there is no clear winner depending on your needs.
The short answer is that if you only want aerial footage, the phantom 3 is a better option. But if you want to shoot both aerial and ground footage, the yuneec 4K camera is still very capable but much more flexible since you can remove it from your quadcopter and use it on the ground..
Why the Phantom 3 Professional is better
I would say that the camera and gimbal on the phantom 3 is slightly better. The phantom 3 gimbal provide better stabilisation (only marginally better) compared to the Yuneec gimbal which is noticeable in very windy weather. THe Phantom 3 uses a Sony exmor CMOS sensor, but Yuneec uses a generic unbranded CMOS sensor. Although technically both cameras can record the same resolution 4k videos, the Sony sensor on the phantom 3 produces much better looking footage.
Why the Yuneec Q500 4K is better
In order to use your Phantom 3 you need to use a smartphone or tablet connected to your remote to view the video feed from your drone. However the ST10+ remote on the Yuneec includes a built in screen running android which provides all this functionality without the need for a smartphone/tablet. In addition to this the camera can be removed and mounted onto the included steadygrip. This means that you can also record stable footage with a 4K camera on the ground which is a very nice feature only available on the more expensive DJI Inspire 1.