All Nikkor AF-S lenses have fast quiet focus using ultrasonic motors, but this is equivalent to Canon's USM.
Nikon does not have an STM equivalence. STM lenses use a stepper motor that allows smoother movements which works better contrast detection based auto focus as used for video AF and mirrorless. The downside is the focus can't jump to a correct focus position as quickly as an USM/AF-S lens. Canon has designed the STM lenses to be very quite for video, but I don't think there is a fundamental reason why the stepper motor would be quieter.
If you are really into video then you will want to be manually focusing anyway with a focus puller. This is where the many nice manual focus Nikon lenses are excellent and much better than any autofocus lens, including STM lenses. STM lenses help with some issues for the point and shoot video type use, but don't change much for those that won't to make a high artistic production video.
Also an external mic will go a long way to eliminating focus Noises.
In general canon spend more research money on video features and their DSLRs are more video focused. Nikon tends not to put so much effort in does OK. There are Hollywood producers using D800's despite the Canon press.