In terms of ISO, is the ISO performance compromised? Say I was using a 50mm DX on my FX body, would I have a lower quality ISO performance vs an FX 50mm on my FX body?
No. The same amount of light goes to the part of the sensor you are using with a DX lens on your FX body, so ISO is not impacted.
When you use the DX lens you use less of the sensor, keeping the ISO / Shutter Speed / Aperture relationship unchanged.
Well, sort of. If you use only part of the sensor — as you do in DX crop mode — you are inherently gathering less light. (The light per area is the same — so your exposure settings are the same — but you have less area.) That means that if you print at the same size as you would an image from an FX lens, your print inherently has less light per area — or, to think of it another way, any noise would be enlarged more than it would be otherwise, and theoretically more apparent.
Of course, this is also true if you crop some area from an image from your FX lens and enlarge. In most practical terms, the difference is so small that no one ever thinks about it.
ISO is all to do with your camera the ISO proformance will be the same nomater what lens is on your camera.
I will say that quality of light has a big impact on noise. ISO 1600 in a dark room will be more noiser (I think that's a word) that 1600 outside in the sun.