Ah, the DX versus FX dilemma, first a lens is always a lens and you 18-200mm is still a the same no matter what camera you put it on, the lens projects an image on the film/sensor plane, called the image circle, being DX means that this circle is smaller in diameter and will not cover a FX full frame format, with DX because the sensor is smaller, it gives you a false sense of magnification, what you have is less field of view and not magnification.
I long ago decided it made a lot more senses to work with Field Of Views in degrees; that entire comforting “equivalent to… on a 35mm” is just annoying and confusing. When looking through a human eye you get a FOV of +/-46 degrees, that would be a 50mm lens on 35mm film, a 75mm lenses on a medium format and 210mm on a large format or 35mm on a DX camera, see what I mean, if you like the feel of a lens, look at its FOV, then no matter what format you choose, just look for the lens with the right coverage for your format.
About the noise, I seriously think that today’s offering from Canon and Nikon well exceed the need of the photographer apart from the most radical deep low light dive. There is a lot of buzz around noise, bottom line is you want to shoot where there is decent light available (either you use the ambient one or you supply your own source) otherwise welcome to blue city. For fast action, pretty much everything in the newer mid range to high end cameras will be more than adequate up to 800 ISO.
