It doesn't seem you read the previous discussion, specifically from posts #75 to #83, i.e., you seem to be repeating what was already discussed and resolved.
I read them several times. I tried to elaborate on the somewhat confused and incomplete responses. The profiles are either available or they are not. You can make your own to supplement what Adobe does not create for you - it takes effort, but if you want to make a meaningful comparison, you can actually go through the exercise of printing the targets and imaging them and using the Adobe software to build your own profiles. Having done this for the 5D + Canon 15mm full frame fisheye, I thought I'd share the information. When you pointed out with your "Of course" comment with red arrows on the screen shot of the lens correction menu, you cropped out the most important part of the screen shot - no profile was available. You can make one available if it exists, or more importantly, if you create it and make it available - that's the reason for the links I included for the OMD user who may not be aware of these resources. I apologize for trying to help the OMD user get the most out of ACR, which is lacking for him at this time.
Since none of us have access to the OMD image used in the example, I can only draw from my own images. DXO and ACR have correction profiles for an obviously distorted combination of a 5D2 (or 5D) and Canon 15mm full frame fisheye. In the most recent incarnation of ACR (7.2) and DXO (v8 ) both are corrected automatically with the manufacturer-supplied profiles based, presumably, on the metadata contained in the file - that is, I do not need to configure anything manually to get the correction applied (in ACR I have to tick the "Enable Corrections" box - in DXO this option is on by default). Both give the user control over tweaking the geometric correction, and both give the user the ability to tweak lateral chromatic aberration and purple fringing. Both give the user the ability to control the crop around the corrected image (ie, addressing the comment above about "wasting" less of the corrected image). Only DXO gives the user the ability to recover anamorphic distortions that may occur under certain lens-camera combinations at the edges of the image.
Since the recent posts seem to indicate that this kind of comparison would be interesting, especially because the point of the discussion seemed to be the ability of both applications to utilize metadata for distortion and lens correction, I hope this additional information is helpful to someone.