Let's not make this difficult. Countertops are not rocket science. I'll try to make this quick about what granite is and isn't and what quartz is and isn't.
Granite - I won't go into the geology behind granite, only the basics as it pertains to the customer. Granite is a natural stone comprised of many minerals. Feldspar, Mica, quartz to name a few. Extremely hard and somewhat unpredictable in it's porosity. Yes, it needs to be sealed, but this takes 15 minutes. If you want perfection, probably not your product. Generally the product will have fissures and pits, although some will have less than others. Don't expect every granite to be perfectly shiny and reflective like a piece of glass.
Quartz - this is actually a misnomer. The industry has basically adopted the word quartz when referring to engineered quartz countertops. Quartz is a man made solid surface and there are a lot of brands out there like Silestone, Caesarstone, Cambria, etc. All are basically the same and all the good brands are made with the same machinery made by Breton. Its comprised of 93% quartz minerals mixed with 7% resin. It's a great product but not perfect.
These are the two top countertop products on the market right now in my opinion one is not better than the other. The pluses and minuses of each play to your personality. If you are worried about having to seal granite, of quartz maybe for you. If quartz looks fake to you, than granite could be for you. Pricing is a big factor too and you can typically get granite for cheaper than you can get really good-looking quartz.
There is a lot more information that I could go through but I think this gives you a pretty good start. I would say make sure the person selling you your countertops is knowledgeable enough to tell you about each product and also be able to read your personality to you find what's right for you.
As always, I'm available to anyone needing info, so if this makes you curious and you have more questions, then come on down to our showroom and I'll be more than happy to answer them!