There might be more than one definition of "Greek yogurt." Fage, which is a Greek company and was the first company to import Greek yogurt to the US on a large scale, has always made the strained kind even when they were just a local Greek company.
Labneh is much thicker and firmer than the Greek-style yogurt we get here. www.fageusa.com/our-greek-heritage/greek-y
Whatever the situation, the Greek style yogurt you get in the US has a different nutritional profile from regular yogurt. It's concentrated, so a cup of it will have more protein than a cup of regular yogurt, and 30 to 50% more calories as well . It has less calcium, though, because some of the calcium gets drained off with the water. I can't find any information about B vitamins, potassium, etc, but I suspect some of those are lost as well.
So it's a trade-off. You get more protein but less of some other nutrients, and more calories. Neither Greek nor regular is "better;" it just depends on what you need and want out of your yogurt.
To answer a question from another thread, the reason Greek style costs more than regular is that it takes 4 gallons of milk for a gallon of Greek yogurt, versus about 1 1/4 gallons of milk to 1 gallon of regular. I've found that yogurt purchased with a coupon is usually cheaper than it costs to make at home, especially when you take into account that you *can* mess up the homemade kind occasionally.