First off, long live Lord of the Rings. I prefer it to HP OR Star Wars. So yes, LotR was the Star Wars of a generation. But that generation was the Greatest Generation. Frodo Lives anyone? Maybe a bit of the Baby Boomers. It brought to life huge worlds for kids. Later it became a great movie, but it was more an adult movie. It didn't shape as many kids lives, because it was aimed a bit older, especially at people who had already read the books. It was a homage to a classic. HP shaped the childhoods of countless, brought books to the forefront, and had a full life as both book and movie independently.
New Star Wars may be lucrative and iconic, but a lot of that is nostalgic, oftentimes dissapointed older people, not the newer generation. Hardly the cultural, defining force of HP, not by a long shot.
Of course were really talking about late gen Y'ers. Someone born during the Reagan years didn't grow up with Harry Potter. If I had to choose something for them, probably Star Wars, original. Besides that, the field was kind of barren.