There is no simple answer. The fact is Full frame will have bigger pixels, so better light gathering capacity and hence better low ISO ability.

If you are able to shoot with a wider f stop and hence able to use a lower ISO, then the noise will be better. You can get f1.8 or wider f stops in lenses in the wide angles. Else f2.8 is the widest for telephoto lenses.

There is ofcourse a 200mm f2 lens. F2 is one stop wider than f2.8

So if you are shooting at f2 instead of f2.8, then you will be able to use one stop lower ISO. f1.8 is one third stop faster than f2.

Remember that the depth of field would be extremely shallow at those wide apertures so unless you are extremely careful in focusing, the image will be soft due to lack of focus.

I find my 5D III (full frame) and 1D Mark IV (1.3 crop) better in its low light ability than the 7D. Just check the kabini leopard images shot with 1D Mark IV and the ones shot by others with 7D and you get a rough idea about noise.

However, remember that if you want to shoot in very low light situations even the f1.8 won't be sufficient. I was waiting for a leopard to appear in the night and the scene needed 40,000 ISO at f2.8. So you have to tell us which scene you are planning to shoot and then we can tell if it is practical or not.

Canon has a 50mm f1.4 which is cheap. The 50mm 1.2 is around a lakh and then there are cinema lenses which are pretty costly.

I have been bitten by Sigma before. Their lenses didn't work with the new Canon firmware. Every time you use a new camera body, there would be a potential chance of mismatch. Canon and Nikon don't reveal the full specs to the third party lens manufacturers. So not always they get it right. The new Sigma 24-105 f4 didn't autofocus well with Canon cinema lenses. Then Sigma changed the firmware and I am told it works now. However, I have decided to only stick with Canon lenses, so all colours match even though different canon lenses were used.