Granite is natural, quartz is man made.
Granite CAN be porous so thereis a risk of stains. If the company selling it will warranty it for stains then you have an out. Just make sure you know what the warranty includes. That said, granite has some amazing colors and unusual patterns. Quartz has many options but are basically symmetrical patterns. If that is more you, than go that route. I do believe that people looking to buy a home sway more toward granite. If you are a purist, that is the way to go. Quartz can be beautiful and may hit the color range you want. These days its typically higher priced. Good luck in your purchase!
Granite has been the typical choice for many years, now there's more of a trend to quartz which is more expensive and easier to care for. It truly is your personal choice of how you'd like your home to look. There are some truly beautiful granite pieces that are unique.
One is not 'better' than the other, there being pros and cons with both. As it is your dollars, at the end of the day, it is entirely your choice.
I do not feel that it can be generalized that househunters prefer one over the other, as LCreative suggested.
Granite is definitely more trendy, but it's also easier to maintain. Granite needs to be sealed periodically. I also discovered through research that granite puts off a gas. It's not noticeable, but I just didn't want that in my home. (personal preference)
I had granite countertops for over 20 years. They were great! Never had any trouble with stains and the price was affordable. Now I have formica countertops and I can't wait to replace them with granite again.
quartz is a little more durable than granite...especially for lighter colors. Ganite can stain and does need to be resealed no mater what the store tells you. quartz also is more scratch resistant. If you're going with a darker color it really doesn't make a huge difference.