How does the dynamic version of an exercise compare with the static version? For example, in the case of the side plank, how results would differ between the two? Is this just a question of personal preference?
There's already an answer to this, sort of, but I'll specifically try to address your question which is a smidge different.
Typically you want to exercise muscles for whatever their role in athleticism or daily life will be. Also, some muscles have evolved to perform certain roles in certain ways. If you need to push a car, it's natural that you'll engage all of your big muscles (quads, glutes) more than your smaller pushing muscles (soleus, triceps). They all work together, but it shouldn't be any surprise that larger and more powerful muscles were designed to handle more of a load than smaller ones.
The abdominals and erector spinae tend to be used in an isometric fashion for load bearing, both just to keep the human body upright and to stabilize the trunk for lifting heavy objects (whereby the prime movers again become the larger hamstrings, quads, etc).
That being said, concentric exercises are generally more likely to result in increased muscle size and force generation, and studies show that simply having larger abdominal muscle tissue creates better posture.
But to specifically answer your question you'd want to do both concentric and isometric ab activities. Isometric because that's generally what your body does all day long and during advanced training, and concentric because it will create stronger and larger muscle tissue.
It's easy to train, and especially when you look at potential back injuries from sit ups and neck injuries from crunches, it's easy to see why it's a go-to abdominal exercises especially for people looking for good-enough fitness (ie: not strength athletes).
If you want to beef up your ab exercises, I'd recommend "churn the pot". Toes on the ground, plank position, elbows on a yoga ball, fingers interlaced or at least hands close together. The smaller the ball, the harder it is.
Move the ball slightly to the left, then the right, then front, then back. You'll quickly feel how hard it is to stabilize.
I don't have specific information related to planks, but in general:
Research shows that the most effective training programs include exercises involving concentric-eccentric repetitions (dynamic exercises).
Isometric exercises are a beneficial alternative for those with joint disorders where dynamic exercises might cause pain.