In the specific example you gave, ie, at f8 (and above -- f11, f16, f22, etc.), one would be hard pressed to see any difference whatsoever in sharpness between two shots taken with lenses of modern design (ie, designed in the last 10 years) and from one of the major camera mfgr (eg, Nikon, Canon). However, the prime might do better than the zoom if there are bright lights in the frame (ie, "resistance to flare"), or whether straight lines are rendered as straight or slightly curved (ie, "lens distortion").
If, on the other hand, you were comparing a kit zoom near its maximum aperture (say, f3.5) to the prime at the same aperture, the prime would likely be noticeably sharper, again assuming both were from the same company, both of modern design, both on a tripod, etc. etc.
However, if you were comparing a modern pro zoom (say, a Nikon 24-70 f/2.8 - $1900) at f/2.8 and 35 mm to say a Nikon 35mm f/2 AF-D (ie, designed in the 1990's, currently being sold for around $325 new) at f/2.8, the newer zoom would clearly be superior to the prime.
To further complicate lens purchasing decisions, one also has to factor in vibration reduction / image stabilization. When one is shooting hand-held, and the light is so low that one has to use wide apertures, it usually also means slow shutter speeds. In the range of 1/2 second down to about 1/60th of a second, a lens with VR/IS (used hand-held) will make a non-VR lens look silly, even if when mounted to a tripod so the VR isn't needed, the VR lens is slightly less sharp than the non-VR lens.
If you are interested in a particular lens, just Google reviews of that lens. There are a huge number of people who obsess over lens performance and many websites do reviews.
Tom