Advantages of using a prime is physically less weight to carry. Primes have faster maximum apertures which allows for lower ISO and higher shutterspeed to better stop action or eliminate camera shake. That faster maximum aperture also allows you better control of depth of field to isolate a subject.

The advantage of the zoom is the various focal length range it offers without having to carry additional lenses. But unless you're using one of the F2.8 high image quality (expensive) zooms, the same focal length in a prime should give you better image quality.

I dislike what has become a misnomer for the use of the word Prime -- which I learned prime lens was the lens which covered the diagonal of the size of frame. Now instead of calling it this the reference is to any single-focal length lens. The topic of which is better also is dependant upon the construction of the zoom - but so far it appears the zooms get close but have not done too much in the surpass of single focal length lenses (except in cases where the cost is bery large). maybe I am just picky? lol