Software Engineer here who loves to draw/sketch. The biggest difference is stroke consistency and handling weight. So an ideal handling weight will let you exert more control over your strokes; your straights are cleaner, your curves are more fluid. Think of how some gaming mouses are weighted.
If you find the right mechanical pencil (i.e., not a cheap plastic one), it wins in both aspects. Plus a mechanical pencil never becomes too short that it does not rest stably on your grip.
But still, there is a certain charm to a drawing produced with the variable stroke widths of a wooden pencil. So I guess it depends what you're going for.
I am not very artistic so never got into drawing or sketching, I do understand the stroke width point though, my school required us to use fountain pens (as a left-handed person, it's probably the the single biggest reason I've avoided hand-writing ever since, what a nightmare!).
I use a Uni Kuro Toga Roulette I got from Japan for measurements and technical drawings I do at home, but I don't do any of that professionally to say how good it is. The key point for me is that it's always sharp every time I reach for it.
I have wooden pencils but when I grab those (infrequently, usually for marking wood or walls etc for DIY), I find they need sharpening, and some times the end isn't pointed enough to mark a wall through a screw-hole. I use them infrequently enough that I rarely bother sharpening them after I'm done, and they get thrown in a drawer or tool box as-is.
If you find the right mechanical pencil (i.e., not a cheap plastic one), it wins in both aspects. Plus a mechanical pencil never becomes too short that it does not rest stably on your grip.
But still, there is a certain charm to a drawing produced with the variable stroke widths of a wooden pencil. So I guess it depends what you're going for.