A few things to consider...
All Adobe profiles are made specific for each camera model. This includes the common "Adobe Standard" profile. So Adobe Standard for an older Canon 5D will likely produce different results than the Adobe Standard for a newer Canon 7D2. Differences between Adobe Standard profiles for Canon vs. Nikon vs. Sony may be even greater. When you discuss profile differences it's important to tell what camera body you use.
There are some key variables at play when making custom profiles. One is the tool used (Xrite or Adobe DNGPE), one is type of light used to shoot the target (direct sun, shade, etc.) and one is the base exposure.
Xrite and Adobe DNGPE have always generated significantly different profiles. The fact that each tool has loyal users only demonstrates that personal preferences vary a lot. Xrite, in my experience, generates profiles that produce much higher saturation. In your sample, the hues vary a little bit, but the main difference is in saturation.
The type of light makes a difference, of course, but it's a suprisingly small difference. It's been well demonstrated that the "spectrum" of the light makes the most difference while the color temp makes little difference. Direct Sun, skylight, cloudy, even flash have different temps, but very similar spectrums. Only when you use tungsten, CFL, or LEDs do you get significantly different spectrums.
The base exposure of the target makes a significant difference. Adobe recommends using the highest exposure possible without clipping. That usually translates to a LAB value of 96 on the white square. In my experience, targets shot at higher exposures generate profiles that produce higher saturation. Lower exposed targets generate lower saturation. In post processing, I prefer to add saturation instead of subtracting it. Especially on images with strong colors that might exceed display and printing gamuts. So I maintain profiles made from lower base exposures of the target image (LAB=92).
Summary-One: There is a lot of room for improvement in custom profiling. Neither Adobe nor Xrite have made any meaningful improvements in their profile generation software since version 1. And isin't it strange that none of the camera makers provide a profiling solution?
Summary-Two: When someone says they prefer one profile over another, that does not mean one is technically better. It just means they have different preferences and they likely used different values when generating the profiles.