So if you are looking to buy a ready to fly quadcopter to carry a gopro there are two main options, the popular DJI phantom 2 and the walkera X350 pro. But if you are not sure what version you want to get then this post will hopefuly help you choose. Also if you have any suggestions, or comments add them below!
Short answer
Overall the walkera X350 Pro is great value for money and offers more flexibility and I would say is the winner. Although the gimbal is not as good as the DJI Phantom zenmuse, you can always use the money saved (X350 is about £260 cheaper) to buy a better gimbal like the FY-G3.
Price
Here the walkera X350 Pro wins by a considerable margin, the basic phantom 2 starts at around £490, going to about £700 with a gimbal. On the other hand the walkera starts at £250 (without a radio though) and is £440 with a radio and gimbal. Since you will be using these for shooting videos with your gopro camera I will be considering the versions with brushless gimbals in which case the Walkera is £260 cheaper!
Winner - X350 Pro - it is about £260 
cheaper with a gimbal
Flight Time
In terms of the batteries, both the dji phantom and walkera X350 pro us a 3s 5200mah lipo battery and both claim up to 25min flight times 
. The phantom’s ‘smart battery’ has a cool feature that lets you see the capacity remaining, but the annoying thing about this is that it locks you in to buying the DJI phantom batteries (for now atleast). On the other hand the walkera uses a standard lipo which is cheaper to replace and allows you to use other 3rd party batteries.
Winner - X350 Pro - only because the battery is cheaper, both have the same flight time though.
Brushless Gimbal
Here, the winner is the DJI Phantom as it comes with a very good brushless gimbal (Zenmuse H3-3D), Not only is the phantom gimbal 3 axis opposed ot the x350 2 axis gimbal, it also has an advantage that it taps into the flight controller IMU in addtion to the gimbal IMU to improve its stabilization. Although the phantom gimbal is considerably more expensive, it does do a better job at stabilization. That said, the Walkera gimbal is far from being terrible as it still provides great levels of stabilization in general, it just sometimes fails when it is particularly windy, or you are doing some crazy flying. However walkera have a 3 axis brushless gimbal in the works so this should further improve the situation.
Winner - Phantom - the 3 axis gimbal provides better levels of stabilisation
First time setup
Both these quadcopters are designed to be easy to use and can be aimed at those new to the multicopter world. However the DJI phantom 2 wins as you literally just need to put on the propellers before you can fly. On the other hand the walkera X350 Pro is similar to the assembly required for the DJI phantom 1, where you to attach the landing gear, and plug in the compass, and then attach the props. The reason why walkera used this approach was to reduce the some of the shipping costs at the overall box is abit smaller.
In terms of gimbal installation I would say that the latest batch of X350 Pro gimbals is much easier to attach as its just a sliding clip rather than finicky screws.
However once the are both quadcopters assembled all you need to do is run a quick compass calibration, and you are ready to fly.
I would estimate the walkera will take you an extra 5-10min before its ready to fly compared to the DJI phantom so its not a huge differance.
Winner - DJI Phantom - better quality manual and slightly fewer assembly steps required.
Hackability
If you like to modify and tweak your quadcopter then the walkera would be the winner. Most of the DJI compatible parts from third parties will fit onto the walkera X350 pro, but because its fight controller is based of the popular open source Ardupilot project, it opens a word of possibilities. If you connect it up to your PC and upload the latest arducopter firmware you will unlock all of the latest features like full autonomous waypoint based flight (only do this if you know what you are doing as it could reset all of the settings on your X350 Pro)
Also the fact that the firmware is open source you can always make whatever changes you want. Also if you are willing to open up the controller and solder some connectors you can also add 2 way telemetry via the long range 3DR modules, or close range via bluetooth.
Winner - X350 Pro - as it uses the arducopter firmware which gives it waypoint capability, and two way telemetry if you are willing to solder some connectors onto the board.
Update - the X350 Pro has now been updated to include a GCS module and a new camera which opens up the ability for fully automatic waypoint based flight and follow me features!
Overall Winner
As with most things, there are a bunch of factors to consider so the above points are some things to consider when choosing which one to use, howver if top notch stabilisation is what you are looking for then you should go for the DJI phantom, but if you are looking for something that still gets the job done and half the cost then go for the X350 Pro. Both these quadcopters are great and I am sure you will not be dissapointed with either. I tend to side more with the X350 Pro because of its lower price. Given that these are quadcopters that fly around unfortunately its only a matter of time till you get abit carefree and crash, you will be not be as upset if you crash a £440 quad vs a £700 one!