The price difference is not just for internal focusing. The biggest factor is that the 70-300mm is an FX lens, while the 55-300mm is a DX-only lens. That means the 70-300 can be used on both full-frame and APS-C Nikon bodies, which generally raises cost.

From the community answers, the 70-300 also has noticeably better build quality: it feels more solid, with smoother zoom and focus rings. It is also reported to focus faster. In image quality, the 55-300 is still very good for its price, especially stopped down, but the 70-300 is better wide open.

So yes, the 70-300 is the better lens overall, but whether it is “worth it” depends on your camera and budget. If you use DX only and want a lighter, cheaper telephoto, the 55-300 is a good option. If you want better build, faster handling, stronger wide-open performance, or compatibility with FX bodies, the 70-300 justifies its higher price.