I haven't tested X-Rite's software, just looked at the video how it works, and looked at the train images above to make an A/B comparison.
As usual X-Rite software focus on ease of use which is a good thing for casual users, but in doing so they miss out a little on Capture One curve handling and possibilities to tune your general-purpose profile to taste. It seems like they really mean to use it for reproduction rather than general-purpose photography. For general-purpose I think it's better to have a more elaborate and configurable way to generate the profiles as you will generate profiles seldom and use it many times in many conditions.
Capture One profiles (or in any other raw converter for that matter) should be optimized for the curve you will use it with most, which for general-purpose photography is not the linear curve. That's why you export both linear and film curve when making a profile with Lumariver Profile Designer, one to get colorimetric data, the other to get the curve that will be used so the tone reproduction operator will work on the proper curve and optimize the tone reproduction for that. Another aspect is that Capture One expects some contrast to be stored in the ICC profile too, that's why Lumariver Profile Designer allows import of the bundled profile to extract curve from there, or you can design your own.
As you can see on the comparison shots the contrast of the X-Rite profile is lower as it doesn't take that into account.
When rendering a profile for linear curve and then using it with the film curve it will sort of work, thanks to that Capture One's working space RGB primaries are chosen well to minimize color shifts plus that the film curves lack shadow dip (further minimizes shifts). The shadow dip is supposed to be in the ICC profile itself though. So I wouldn't say it's a high-end way of making general-purpose profiles, and it's not how the Capture One bundled profiles are made either. They're not made for linear reproduction with a curve slapped on, they are made specifically to be used with the film curve, and then instead work a little bit worse with the linear curve, but that is how you want a general-purpose profile to be. For their digital backs Phase One have bundled separate reproduction profiles by the way.
Another aspect to look into, which is not evident from the train images, is how the profile makes gamut compression and roll-off bright colors to clipping. Capture One (or really virtually all raw converters) expects the general-purpose profiles to have some gamut compression built-in, and I'm not sure X-Rite is doing that or not from these images. If you make a reproduction profile you don't want any gamut compression at all of course, so I'm guessing they don't do any.
Otherwise one can see that Capture One bundled renders warmer hues compared to X-Rite. This is because X-Rite is more correct on the hues, Capture One's bundled look is generally quite yellow, which you may or may not like. Personally I prefer more neutral rendering than Capture One's bundled profile, but I tend still to manually tune the residual errors so they go towards warm especially on the reds and blues. Deep blue is difficult by the way, if you keep that reproduction accurate it becomes very dark, so almost all general-purpose profiles lighten it considerably for better although slightly less accurate tone reproduction on screen and in print. Many of those little aspects are taken into account when making a good general-purpose profile. General-purpose profiles are weakly output-referred (ie they take into account that they will be displayed and printed, but are not strictly locked to a specific color space), while reproduction profiles are colorimetric scene referred to be able to copy artwork and similar. These are quite different.
To summarize, it seems to me that X-Rite's profile maker is best suited for casual reproduction workflows, while not ideally suited for making general-purpose profiles.
(Unfortunately Capture One v12 has currently a bug in the transfer function export so profile making doesn't work with that version yet, I guess X-Rite's software is affected too, so one have to use v11, the resulting profiles can still be used in v12 though)
