I shoot in the studio with both a D800E and a D610 body, with a variety of lenses, most often a Nikon 24-70/2.8G AFS or a Sigma 35/1.4 Art.
The zoom is quite nice and honestly with the D800E I don't have any AF problems with it using AF-S, and one of the central sensors. It will on occasion "miss", but we're talking less than 1% of the time. Same for the Sigma, or for that matter, any of my other AF lenses.
The D610, however, has been a bit more of a struggle. I find I have to slow way down and very carefully select my AF point and make sure the body has focused correctly before taking the shot. Consistency with the same lenses is not at the same level as my D800E by a long shot. I actually think when I was using my D7100 as a second body that it (by virture of a better AF system) had better AF consistency in terms of shot to shot.
My best guess is that under the relatively dim (compared to outdoor light) illumination of modelling lights that the more consumer based AF system of the D610 may struggle a bit relative to the better AF system of the D800E, D7100, D700, D300 etc.
BTW, I have had a pair of 24-70's and both were excellent. They are not that amazing at 24mm, but from 30-60mm at any distance and 28-70mm at closer distances, they are very close to the performance of primes. I have tested this lens extensively and thoroughly, so I don't make that statement casually. While I do tend to use primes a bit more on the demanding D800E body, I would have no problem at all if I only had the 24-70 to produce very high quality professional work.
-m