Is there anything that makes such a lens inherently better performing than the slower zoom lens in terms sharpness, transmittance and other parameters?
No. Sometimes the prime may be better at a specific aperture than the zoom, sometimes the zoom may be better at the same focal length and aperture. "Better" could be in terms of things such as how "sharp" it is, vignetting, geometric distortion, flare resistance, chromatic aberration, etc. Or maybe one makes using the kinds of filters popular with landscape photographers easier than the other which has a bulbous front element that makes using filters difficult or requires internal rear mount filters?
Or there is no such dependence and speed of a lens doesn't dictate any other of it's characteristics and thus every comparison of lenses should be done on individual case-by-case basis?
That is correct. Every lens comparison should ultimately be done on an individual lens to individual lens basis.
I've used an extremely cheap 35mm f/2 lens that was awful blurry wide open. It had to be stopped down to around f/4 before it got reasonably decent. Even at f/5.6 it was still slightly worse than my 24-70mm f/2.8 zoom at 35mm and f/5.6, and the 24-70 is pretty sharp even at f/2.8. Of course the zoom was about 14X the cost of the cheap 35mm. After only a handful of uses the cheap 35mm refused to stop down no matter what aperture was set in-camera. So it is now essentially useless stuck wide open. It's not even heavy enough to make a proper paperweight.
On the other hand, I've got a nicer 35mm f/2 lens that cost between one-third and one-half what my 24-70/2.8 did, and it's very good wide open.
- It's probably a tad bit sharper than the zoom at f/2.8 and other wider apertures both share in common, though both are really good.
- It's useable at f/2.
- It has IS, something my 24-70/2.8 does not.
- It is much smaller and lighter than the f/2.8 zoom.
But by the time I've bought a 24/2.8, a 35/2, a decent 50/1.4, and an 85/1.8 I've spent well over what the 24-70/2.8 cost me. Sometimes the zoom works better for me, sometimes a couple of the primes do.
Cheaper primes, like the "nifty-fifty" lenses sold by most camera makers, tend to be soft wide open (though not nearly as bad as that Yongnuo 35/2). They need to be stopped down to f/2.2 or f/2.5 to get even close to the same optical performance as a 24-70 zoom at f/2.8. But in terms of bang-for-the-buck, it's hard to beat a "nifty-fifty'! High quality primes have moved into the same price range that good constant aperture f/2.8 zooms used to inhabit. But now the price of the zooms has, if you'll pardon the pun, zoomed plumb out of sight! So by the time you buy 2-3 mid to high end primes you're spending more than what you'd spend on one good f/2.8 zoom in the same focal length range.
In the end it comes down to a comparison of the two lenses in question, how much performance you need the lens to offer, personal preference, and budget.