Canonical is also privately held and not publicly listed.

For sure. The difference is in who the owner is and what their track record in regards to FOSS is. Putting the 19 years of BDFL's Canonical ownership together, I think he's generally been okay. The core products have always been open source and free for both commercial and non-commercial use. I don't know much about the private equity firm currently holding SUSE.

And it looks like this is the same private equity firm that owned SUSE fully before taking them public. (Marcel LUX III SARL is a holding company owned by EQT Private Equity.)

I guess that's a positive, but we really don't know what direction they'd take once the curtains close. Chances are profit maximization will be at the top of the list. It's unknown how that will translate in reality in the short and long term. E.g. would they be nice and give stuff for free early to steal customers from RHEL, tightening down the road, or cutting costs today to make a buck now. It's anyone's guess.