The ribeye is cut from the rib section of the animal — ribs 6 through 12 — a part of the cow that does relatively little work. That means the muscles stay tender, and more importantly, fat deposits throughout the muscle rather than around it. That intramuscular fat is marbling, and the ribeye has more of it than almost any other steak on the animal. When you cook a ribeye, that fat renders and bastes the meat from the inside, producing a richness and depth of flavor that is essentially impossible to replicate with a leaner cut.
The New York strip comes from the short loin, specifically the top loin muscle. It sees slightly more activity than the ribeye's source muscles, which means it has a firmer, more distinct grain and less intramuscular fat. What it has instead is a cleaner, beefier flavor — less butter, more steak. A well-aged NY strip from a quality source has a satisfying chew and a flavor profile that ribeye loyalists will call lean but strip loyalists will call focused. Both are correct.
On price: ribeye commands a premium because the marbling creates a more dramatic and forgiving eating experience. A slightly overcooked ribeye is still good. A slightly overcooked strip is noticeably less forgiving. If you are cooking for someone who does not have experience judging doneness, the ribeye is the safer bet. If you are a confident cook who wants a cleaner flavor and slightly better value per pound, the strip is the answer. As a working butcher, when I am picking something for myself on a Tuesday night, I reach for the strip. On a special occasion, the ribeye wins.
One technical note: bone-in versions of both cuts — the bone-in ribeye (cowboy steak or tomahawk) and the bone-in strip (Kansas City strip) — cook more slowly and with better heat distribution than their boneless counterparts. The bone also adds flavor to the meat immediately adjacent to it through the cooking process. If you have the budget and the pan space, bone-in is almost always the superior choice. The theater of it doesn't hurt either.