DPP, LR4 and 5D MKIII
I haven't used DPP for awhile, but my understanding is it will try to apply the same adjustments that you selected to create the in-camera jpeg (and I think you can adjust those, as well). So, if you didn't have noise correction turned off in the camera, it will apply the same noise correction as you had selected.
On LR, you would need to go to the noise menu and play with the sliders.
I've heard several people say that DPP does a better job on the 5D3 with noise than LR using the default settings. I may have to play with DPP again. I really prefer the LR flow, though, and I hate the idea of having to work with TIFF in LR rather than RAW.