Prime lenses are generally sharper due to the reduced diffraction by not having the extra lens elements required for zoom lenses.

A prime lens, even a cheap one, is a master of one focal range, that's all it needs to do and generally, it does it as well as the glass permits.

Whereas, a zoom has to get it right over a much larger focal range, in other words, be a jack of all!

Unless you are paying for professional quality lenses, you will find, when you compare like for like, there is a noticeable sharpness with the prime lens.

The picture with the prime has a creamier background and this makes the flowers pop more and subjectively creating a more pleasing shot. The one with the zoom, is still a good shot, but within the confines of what the zoom can produce with regards to both, sharpness and background blur, both of which are below par when compared to the prime lens.

If you are still unsure and believe that there maybe another issue, then you need to look at Mico adjusting the lens. 

Sometimes, lenses can back focus or front focus and some new cameras have a setting which allows you to make small adjustments to get the focus correct. You will need to check the manual.

Personally, I believe that the prime is just the sharper lens