As you probably know the basic difference is that granite is natural stone taken right out of the earth, polished, and cut intos. Quartzs are made of real also, but in combination with manmades, so you get the hardness and beauty of real stone, with the consistency and durability of manmade products (kind of the best of both worlds).
And here's the deal - is really trendy right now, but I would never put it in my home (fors). It is a delicate surface that is susceptable to heat damage, acidic damage, and is fragile.
-If you drop a heavy glass jar (for example), or put weight on a large overhang, your granite can crack/fissure/break fairly easily, which make it not ideal for high-traffic areas.
-If you use the wrong type of cleaner (usually those containing ammonia), you will etch the finish of yours, creating dull-looking spots.
-If you forget to use a trivet and have a hot pan/griddle/grill on yours, you will leave a permanent mark (more so than say with laminate tops).
-You also have to periodically reseal tops to maintain their finish
-If you do create damage, it is very costly to bring in someone to repair it. And in most cases they have to patch in a new piece of granite to replace the damaged piece. And since this is natural stone with unique coloring and features in every batch, guess what? Patched in pieces almost never match up with the original stuff.
-Will always have visible seams
Plus the stuff is expensive! Generally a fair bit more so than most Quartz products, although that can vary based on what "color group" you choose from.