Well, considering the number of national hashgachos in the US, it stands to reason that some folks might prefer one over another.
But, more to your point, I’ve heard from certain Chareidi individuals that they are not happy with hashgachos that certify non-cholov Yisroel products. In other words, it’s not only of the OU they disapprove.
I don’t know whether the same people would eat parve products under such a supervision.
Personally, I – for whatever that’s worth – do consider the OU to be a top-notch kosher organization. It is my understanding that many other “heimeshe” hashgochos in turn depend on the OU, especially regarding their commercial ingredient lists.