We know that rodents enjoy running wheels because they use them voluntarily. It's not surprising that the exercise they enjoy is the one that seems to produce the most benefits.
For humans: Doing any exercise is better than doing no exercise. Doing frequent exercise is better than doing infrequent exercise.
The most important thing is to pick an exercise that you enjoy, so you'll be more likely to get out and do it and less likely to come up with excuses to skip a day.
Even better: Find an exercise that includes some social activity, even if it's just getting outside and seeing other people in passing as you run past or being in a gym near other people. Social exposure is great for mental health, so combining it with exercise is a good one-two punch.
We do have some human studies on BDNF (measured via serum, because we can't get into human brains obviously) and exercise: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3772595/ They didn't study different types of exercise, but they did find that longer duration exercise produced greater elevations of BDNF. You don't have to run marathons to capture some of this benefit. A long walk is good enough to get started.