According to Bill's numbers the V1 at ISO 800 is just a hair better in performance than the D90 or D700 at around ISO 2000, or about 1.3 stops. If you add the 1.3 stops to the f/1.8 you end up back around f/2.8.
A Nikon 1 CX format at 110mm about equals the DX FOV at 200mm.
The V1 @85mm f/1.8 would have about the same noise but 3/4 stop less reach than DX at 200mm f/2.8 if you define reach as a function of stops, where 41% more focal length equals one stop more reach.
The V1 with a 105 f/2 would have comparable reach as the 200mm DX but about 1/3 stop more noise. And in a Nikkor you are back to a $1000+ lens.
(edit: the 105/2 DC is screw-driven and therefore would not AF with the V1)
The V1 would have less shutter noise which might be a big benefit in a theater situation. Except at a school play where I would imagine it is like the runway of a fashion show
The V1 would have a significant DOF advantage here (something interesting to think about since in these cases thin DOF is not the "feature" many FX users crave). At 105 f/2 the V1 would have 6.83ft DOF verses 200/2.8 on DX at 4.81 ft.
That is an unfair advantage since the V1 should be shooting more like 110mm f/1.8 for comparable performance. There it would have only 5.54 ft DOF, should such a theoretical lens exist. Still a bit better than 4.81 ft.
Those DOF numbers are from the calculator at dofmaster.com. They use a different COC (0.02mm) than Thom Hogan's worksheet (0.016mm) for DX, which I used for the calcs on the previous post.
Bill's chart suggests roughly a 1.3 stop difference in performance with the V1 around ISO 800 or so, verses D90/7000. But the V1 chart is decidedly non-linear. For example, at ISO 100 the V1 is about equivalent to the D90/D7000 at around ISO 636, or around 2.5 stops.
As a result its performance varies considerably depending on the specific ISO you want to compare.
DX has about 3.2 times more sensor surface area than CX, and that suggests a difference of 1.7 stops.
It is likely that the V1 has some "mandatory" noise reduction going on at high ISO's. It is likely that the V1 will perform at least 1/3 stop poorer than what I suggest above, relative to DX, considering all else - including any enforced NR - equal.