Which is better, the Nikon AF-S DX NIKKOR 55-300mm f/4.5-5.6G VR Lens or the AF-S VR 70-300 f/4.5-5.6G IF-ED?

The 70-300mm AF-S VR has a couple of significant advantages over the 55-300mm. It is an FX lens, which may benefit you in the future, whenever Nikon brings out a consumer-level FX DSLR. Most importantly, it autofocuses faster than the 55-300mm. If you are shootings sports, or anything where the subjects are constantly moving, that would be a deal-breaker.