Which of these lenses is better?

Http://www.amazon.com/Nikon-70-300mm-4-5-5-6G-Digital-Cameras/dp/B000HJPK2C/
http://www.amazon.com/...00005Y3OM/
So theoretically, these lenses are very similar. It seems like the first lens has vibration reduction and a built in autofocus motor, but that's it. It also seems like the second lens would be better in lower light conditions because of the lower F rating. I don't need an autofocus motor or vibration reduction, so which should I get?

You answered your own question.

VR is very helpful in keeping the image tack sharp when focusing at subjects very far from you. Any slight movement from either you, the subject or anything in between will cause blur. Autofocus, well I too can live without it but I bet the second lens is capable of it with the right body. I'm assuming you an a low entry-level camera model. The difference in maximum aperture is very slight, only a half-stop. To me that's insignificant at those values.

It's just VR then that's significant between the two and since you mentioned you don't need it, your choice is clear. Get the second. I'm pretty sure it costs much cheaper too. Perhaps you can get a 50mm f/1.8 for speed with the change. Now that's what you need for low light.

There's not a lot of difference between f/4.0 and f/4.5 - only 1/3 stop.