One other thought, and others may disagree with me, but I think if you are just going to do the normal length safari, I do not think it is worth extra to pay for a private car. Unlike in Africa where the drivers have a lot of freedom, in India, they are mostly sticking to a path to try and find a tiger, which is what everyone wants to see.
We did however pay extra to have the private 1/2 day tour and enjoyed that since we could see different zones within the park on the same drive and our batman came with us to serve a snack.