Let me start by telling you the pros and cons of both surfaces. Neither quartz nor concrete have visible seams. Quartz is more forgiving with hot pans and does not need to be sealed.
Concrete, on the other hand is more flexible with shapes, inlays, edge and color options. Concrete needs to be sealed regularly, but when it is, it, along with quartz is stain resistant. (Tobi Gairley- quartz)
Personally, I like, have used and would continue to suggest both surfaces.
I like using quartz when I want a light color and a clean look. It is far more stain resistant than other light surfaces like certain types of marble. (This is for a kitchen- I feel comfortable with the stain resistance of marble for bathroom use). The marble above, for example, is gorgeous, but I am way too practical to put that on a kichen counter. If I wanted that clean modern look, I would probably go with quartz, even though it lacks the natural movement and beauty of marble. I would worry that my client would hate me after the red sauce or red wine spilled and curse words associated with my name would be flying around the kitchen. If they insisted on it, I would make them sign all kinds of waivers. ;-)
I like using concrete when I am looking for a more distressed “used” feel, or a more “industrial” feel. I would pair concrete counters with a distressed hardwood floor, or a chiseled edge travertine, or a brick floor.
Quartz is a surface I would use if I didn’t want the counter to be noticed. If I had a busy backsplash, and other points of interest in the room, and wanted the counters to blend in and not stand out, I like using quartz. (If the home is very modern, and I am looking for a bright unnatural color, like blue, this doesn’t apply- but for most homes- this would be my thought process.) I would pair quartz with a clean straight edge floor.
I would consider concrete to be more casual and quartz to be more formal. If low maintenance is of highest concern for my client, I would go with quartz. If my client were looking for a lower cost, I would go with concrete. (It is not always lower- but I could probably make it lower by making it very simple.)
I hope that was helpful. They both come in very different looks. It is a decision I would make in conjunction with selecting the backsplash, cabinets and floors. Go select the backsplash first. It might make this decision for you, by clearly coordinating with one surface better than the other.