If you shoot RAW, the in-camera lens correction is not directly applied to the RAW data, it is appended to the tagged data. The lens correction is applied to the in-camera preview JPEG thumbnail viewed on the camera's screen. If your selected camera output is JPEG then the in-camera lens correction is applied at the time the file is processed in camera. As with many parameters, by saving to a RAW file you have the choice later of what correction to apply and by how much. Using DPP you can choose to apply, for example, any CA correction value between 0-200. You can also adjust Blue and Red correction separately. The optimal setting will depend upon the amount and type of CA exhibited in each photo. In general disabling in-camera corrections will save a little in-camera processing time for each image. Applying the correction in post processing allows you to optimize the settings at the expense of your time to do so.
If you open the RAW files in Canon's Digital Photo Professional (DPP), the file with be opened with the in camera settings applied, but may be modified using DPP without any loss of original data. Whether other RAW software uses or ignores the in camera settings is up to the software. LR and DxO apply their own data, so the in camera settings would make no difference if you use those programs to process .cr2 files.
Canon also has added the Digital Lens Optimizer option in DPP (ver 3.11.10 and later). This is similar to what LR and DxO do where the results of specific tested combinations of cameras and lenses are applied to the image. The difference is that Canon is not compelled to reverse engineer any of the proprietary information relating to the camera's sensors and AA filter, the lens' characteristics, the demosaicing algorithm, etc.
A post at Fred Miranda discussed this shortly after it was released concurrently with the 5DIII and the example pics, intentionally shot at f/16 to test how well DLO deals with diffraction, are fairly impressive, especially given that on the forum post they have been re-sampled (by tinypic). The downside to DLO is that applying it takes some intensive processing and the size of the RAW file is doubled. If you later turn DLO off for that image, the RAW file returns to the original size. Some have speculated that a "duplicate" RAW file with the corrections applied to the RAW data is added.