I am going to ASSUME that you are delivering to the web...
If you go with the D7000 combo you will get:
!. About 1 stop advantage going to the new body 2. About 1.5 stops with the new glass. 3. You might also get about .5 a stop advantage when you shrink the image down to web size.
Going the other way with the D600 you'll get:
1. About 2 stops going to a modern FX sensor 2. More magnification optically since you'll be at 30mm instead of 200. 3. Probably cose to a stop better noise reduction by shrinking that image back down.
If you plan to make large prints, then this scenario changes somewhat. But either way, you should see at least a 2 stop gain over what you're doing now. Sadly, this scenario highlights exactly what a penalty slow glass exacts for this kind of work. It ALWAYS hurts the scenario...
Given your scenario, I'd buy the D600, and try to save for better glass. The D600 will reward every future glass purchase more than the D7000 will. It's got better color performance, better dynamic range, and better ISO performance. Not to mention more megapixels which will help if you print large or shrink down images for other uses.
>So this is my doubt: The specific need that makes me think >about upgrading is taking pictures of my children’s school >presentations indoors at night (dance, theater plays, etc) >when light is low and I am sitting somewhere in the back of >the auditorium. I am currently using my D90 in ISO 1600 and a >70-300mm VC 4.0-5.6. What is likely to get me more improvement >at the long end: 1) using a D600 in ISO 3200 with my 70-300 >4.0-5.6 VC or, 2) using a D7000 in ISO800 with a 70-200 2.8 >I guess the cost of a D600 is more or less the same of D7000 + > a Sigma/Tamron 70-200 2.8, so, is more a results than cost >driven decision.