This is very much personal preference but I do think there are some pros and cons to both. For photography I generally prefer to use a fixed density filters as you are given a specific value of light that is blocked making it easier to do the calculations on your new shutter speed. The downside is obviously that you probably want more than one density of filter because different environments call for different shutter speeds (see below).
Variable ND filters are incredibly useful for videography as they allow you to maintain an optimal shutter speed, ISO and aperture using the variable filter to affect the exposure as light changes. I don't use variable ND filters for photography as they don't give a specific read out of how dark they are just a sliding scale of 'darker-brighter' making calculations on shutter speeds more difficult.
This is very dependant on what you will be photographing, the time of day (light) you will be photographing in and the look you are trying to achieve. An example: If I was to photograph a seascape after sunrise in reasonably bright conditions my shutter speed without any filters might be say 1/200 of a second.
3 Stop Filter - 1/200 will only be slowed down to 1/25 which is not really slow enough to capture blur much motion in our shot
6 Stop Filter - 1/200 will be slowed to 1/3 of a second which will slightly smooth the spray off waves or give a feeling of movement without completely smoothing it.
10 Stop Filter - 1/200 will be slowed to 5 seconds which is enough to start flattening out waves and motion.
How I use my filters:
3 Stop - City and street scenes to achieve slight motion blur in cars, bikes, pedestrians to give a shot 'mood'
6 Stop - Waterfalls or very fast moving waves when they crash on the rocks
10 Stop - Seascapes and Landscapes where I want to smooth out the motion to create a calmness in water or a streakiness in moving clouds.