A few words about this question...

2-axis gimbal.

 

As you know this kind of the gimbal stabilize camera movements in two axis - roll (tilt left-right) and pitch (tilt front-back). Doesn’t stabilize rotation in yaw axis (horizontally rotation left-right).

Advantages:
- usually lighter construction than 3-axis version,
- stabilize two most important axis which can be enough in typical application,
- you can control tilt axis using radio - tilt camera down or up,

Disadvantages:
- doesn’t stabilise yaw axis, (3rd axis)

If your copter is well made, this setup may be enough in most of applications. TIP: you can use deshaker and stabilize yaw axis only in the post-process. Results may be very good.

Products:
2-axis gimbal 
landing legs 
dampening system

3-axis gimbal mounted to the frame (under the frame):

This kind of the gimbal will do everything you need - stabilize all three axis, giving great video results.

Advantages:
- stabilize all three axis,
- you can control tilt using the radio - tilt camera down or up,
- you can control yaw using the radio - rotate camera left-right independent from the copter position,

Disadvantages:
- usually heavier construction than 2-axis ver,
- requires retractable landing legs if you want to rotate the gimbal, (otherwise landing legs may be visible on the video footage),

Products:
2-axis gimbal
strong 3rd axis
landing legs
dampening system V3
dampening system V4

- 3rd axis motor,

 

3-axis gimbal mounted to the rotating landing legs:

(Recommended design for PRO Video/photographers.)

dvantages (like previous setup and...):
- it's safer than retractable legs - legs are always in landing position,
- doesn’t require extra servos and power to the rectangle landing legs system,

Disadvantages:
- ?

Products:
2-axis gimbal
3rd axis mechanism
- landing legs: foldable or light legs - recommended 315mm long 
dampening system 

- 3rd axis motor,

 

Which one to buy?

1. Typical application, possibly some post processing will be required - 2 axis.

2. If you need stabilized video straight from the camera, but you don't want to control (rotate) yaw during the flight - 3-axis with non-retractable legs mounted to the arms is a perfect setup.

3. If you need stabilized video straight from the camera, and have option to control the yaw (independent with second operator or by yourself) two setups are possible:
- Gimbal with 3 axis and retractable landing legs, 
or
- Gimbal with 3-axis mounted to the 3rd axis rotating legs (recomended).

 

Just my two cents based on my experience :) 

Jakub Jewula