The Tamron 70-300mm f/4-5.6 Di VC USD Lens incorporates Tamron's first implementation of "USD" or Ultrasonic Silent Drive. My first thought is that the words Ultrasonic and Silent are redundant as far as humans are concerned, but ... the lens does focus quietly (though not completely "silent"). The 70-300 VC's focus speed is not especially fast.
Combining a somewhat slow AF speed with a relatively narrow aperture means that this lens is not the best choice for sports photography. The Tamron 70-300 VC will work best in this regard when shooting a subject that remains a near-constant distance from the camera under a healthy level of daylight.
Much more problematic is the inconsistent focus accuracy I'm experiencing from the Tamron 70-300 VC. I had to spend a more-than-usual amount of time focus testing this lens - just to confirm what I was seeing. And my determination is that my Tamron 70-300mm f/4-5.6 Di VC Lens (purchased retail) is very inconsistent in the focus accuracy department.
I have used the 70-300 VC on multiple Canon EOS 1Ds Mark III bodies and on a Canon EOS 60D with similar results. Some shots are focused accurately while backfocusing occurs as frequently as frontfocusing. With their deeper DOF (Depth of Field) with identical framing, APS-C camera bodies will not show the focus errors as readily as full frame bodies.
The bottom line is that even a sharp lens does not deliver sharp subjects if not focused accurately. Focus accuracy issues were realized in the field - and they made evaluating VC difficult as I had to discern whether the cause of blurred shots was mis-focusing or camera shake.
Automatic focusing speed as a tele zoom kit lens is actually quite fast. Reasonable fast at least for anything from normal shooting to surprise seagulls attack. I would say that this lens is probably the fastest focusing Nikkor kit tele zoom lens currently on the market.
AF isn't as fast or as silent as Nikon's pro lenses that sell for ten times as much, but considering how tiny and inexpensive this lens is, it's very good.
AF is smooth and reasonably fast and sure. No AF telephoto can track fast action at only 5 feet away, but at reasonable distances as we see in kids' sports and stage shows, it's swell.
Likewise, when subjects like birds are at reasonable distances, it can track them, too.
Autofocus on still subjects fast and sure.
Autofocus is slightly slow considering that these lenses are designated AF-S. I can also induce this lens to hunt for focus in low light with off-center sensors. Even in bright light this lens isn't a snap-to performer when it comes to focus. At 200mm, the f/5.6 aperture is also pushing Nikon's AF system to the limits, so off center sensors sometimes will cause the lens to "double-clutch" at the focus point (do a secondary refocus).
Just like all recent Nikkor lenses it features an AF-S motor (silent-wave (ultrasonic)) so AF operations are near-silent although the speed is a bit on the slow side. The AF accuracy of the tested sample was very high.
I've been using A005 with Nikon D700 for 5 years. The AF speed is reasonably fast and the accuracy is top notch. The VC is even better than Nikon's VR. However, there are user comments ... FF bodies have more powerful focus capability than APS-C ones.
When putting in Canon bodies, the story (especially regarding AF accuracy) could be different.