I've only eaten at the New York New York Nathan's once. The MGM Nathan's is usually where I go to get Nathan's since I usually stay at that hotel. They're pretty much the same in business, service and quality.
Nathan's is good for your easy, fast, cheap food in Vegas. It definitely beats the average hot dog. The fries are 'meh'. I can go without those. I've had their wings before and those are ok. Stick with the hot dogs. It's what they're famous for anyway.
If you just lost a bunch of money to gambling or you're on a low budget coming to Vegas. This works for you.