I've been to both aquariums. In a direct comparison, I think the NE Aquarium comes out on top. However, the NY Aquarium is well worth a visit.
The NY-Coney Island aquarium currently has a rather large exhibit entitled "Alien Stingers" It is one of the few permanent displays of jellyfish in the US - something you may not have at NE Aquarium. For me, this exhibit alone was worth the trip and admission price. I was also very impressed with the seahorse, octopus, and nautilus exhibits. If you like penguins and sea lions, there is a large Pacific sea cliff exhibit with scheduled feedings.
Coney Island itself is a rare gem of Americana and an interesting part of the New York experience. The boardwalk has cool breezes, street performers, ice cream cones, and Nathans hotdogs. There's also the amusement parks, penny arcades, and a turn-of-the-century hand carved carousel that the city recently saved from demolition.
A pic of a jellyfish. The pic doesn't do it justice. It was amazing to see it pulsating and changing color in person!