I suspect the color profiles are not the same and you would have to be sure you could disable all processing to compare between the two I would think…
Edit 
This came from a poster on the Canon forum and basically sums it up…
Based on my experience with other (than DPP4) post-processing software there are 3 different kinds of profiles the pertain to raw processing. They are referred to as Input Profile, Working Profile, and Output Profile.
Output Profile is the ICC Profile that gets embedded into the metadata (if desired) for the resulting image file.
Working Profile pertains to the color space used during editing.
As I understand it Input Profile pertains to the camera used to shoot the picture, which I assume to relate to the sensor since NOT much else matters in the case of raw files.
DPP4 allows some choice for Working Profile. Those choices appear to be sRGB (default I think), Adobe RGB, Wide Gamut RGB, Apple RGB, and Color Match RGB. I don’t see any way to specify or choose an Output Profile. What I get in the resulting image files is an ICC profile named “sRGB v1.31 (Canon)”. However, there is NO mention anywhere about an Input Profile.
In the case of Rawtherapee (example of other post-processing software) it is possible to select DNG Color Profiles (i.e., .dcp files) which are produced and distributed by Adobe. It is believed that these files serve the same purpose for the various Adobe products that support post-processing of raw files. Apparently, these files do NOT conform to the ICC standards for color profiles but, I believe, they contain the equivalent information plus some. These DCP Profiles are camera specific and there may be several for each camera that appear to relate to the various picture styles that the camera offers and is presumed to pertain to what gets used by the camera to produce camera developed jpg files in those picture styles.
Insofar as these DCP Profiles are produced by Adobe rather than Canon it certainly is fair to question how they go about creating such files for all of the vendors whose cameras are supported by their software. One would be inclined to think that all of the various camera manufacturers assist with this effort. However, I can provide no evidence to that effect.
In summary, it does seem to me that Canon does NOT need to produce individual profile files that conform to the ICC standard (i.e., ICC Profiles) in order provide the equivalent information to its’ own software. However, it would seem that Canon could/should be willing to inform its’ customers about how this is done. That might be all I’m asking for!