I've never noticed any difference. In my experience, VR consumes more juice, but I have never heard anyone say that the AFS lenses are easier on the battery than the older AF-D lenses.
Two other points to consider:
1. Not all AFS lenses are equal. The top of the line pro AFS zooms and primes focus much faster than the slower consumer AFS lenses. I think (although I don't know this for a fact) that this is a function of a slightly less robust AFS motor, and the slower (darker) aperture. That said, the AFS 80-200 f2.8 is a top-shelf lens. It has the fastest AFS system available at that time.
2. Not all of the AF-D lenses are slow focusing. The 80-400 VR is a notorious dog. But, my small AF-D primes are quite fast, though slower than their AFS cousins. Like I implied above, the 80-200 AF-D 2-Ring Tripod Mount lens focuses very fast for a non-AFS lens. It was the undisputed king of lenses of it's focal length in it's day, and was used for many sports photos.
The non-AFS lens sells new for about $1,100, and used for about $800. The AFS version sells used for about $1,250. The generation newer 70-200 AFS VRI sells used for about $1,600. These price intervals make it a really tough call. Maybe the way to look at this is to decide what you're going to shoot, first. I would say that if you are going to shoot football or baseball with a D800 or D4 body, primarily in daylight, then the 80-200 AFD Tripod Mount, bought new with 5-year warranty or used to save $200 is more than adequate. if you are going to shoot basketball indoors, or football under lights, or with a D7000 or even a D600, then I would recommend one of the AFS versions (that is what I will be using it for). If you think you might need VR, or want to use a teleconverter (though I think the TC also works with the 80-200 AFS), then the AFS 70-200 VRI is the best option.