Mmmmpf. These threads show up regularly, but I think nobody ever discusses the real advantages and disadvantages.
The following is only my opinion, of course:
A good axe has a lot more power (a LOT more) depending on size and weight. If you compare a 20" hunters axe with a 10" bladelength chopper, there isn't even a comparison. But a long chopper is much, much faster. On anything that doesn't give resistance to the blade, any branch up to 1.5" diameter for example is much easier cut with the chopper. The axe is in many cases too slow to cut it free hanging, so you need to put the branch on a support which is inefficient. The difference in efficiency is huge. On the other hand, any target that gives sufficent resistance to the blade, any larger branch, any branch close to the trunk, a tree etc. is much easier chopped with an axe.
There are the cutting competitions where choppers appear not far behind an axe, but the problem is that these tests and competitions are severly time limited. In 10 seconds or even a minute a good large chopper will come at least close to an axe or hatchet because it is faster and you can take more swings in the same amount of time. But it will cost you much more strength. Try the same, chopping continuously for 30 min. Fatigue will set in and you will take approximately the same number of swings with the axe as with the chopper and due to the much greater power delivery the axe will pull WAAAAAY ahead. But again that applies only to "hard targets". On soft targets always the chopper.
I have tested the RD9 and the Wetterlings hatchet against each other that way, they are almost the same OA length and weight. On heavy chopping the RD9 doesn't stand a chance. RD9 against 20" Wetterlings hunters axe and the comparison becomes useless, because they are so unevenly matched. But cleaning out a tree I have the RD9 always close at hand. It will cut cleanly through 1-1.5" freehanging branches, and is many times faster for that job than any axe.
Splitting, I usually prefer batoning the chopper.