I don’t know about American hechsherim.
In E”Y there is a huge disagreement over this. Everyone has their own hechsher….
* Edah HaChareidis: Yerushalayim, accepted by pretty much everyone except a few isolated political types. Personally I have never met anyone who didn’t use Edah for kashrus reasons.
* Rav Landau: Bnei Brak, seen as highly reliable, but many Litvaks refrain from using it because he is affiliated with Chabad. Aside from that, everyone I know uses Rav Landau’s hechsher.
* Sheeris Yisroel: Bnei Brak, Litvishe hechsher. Many chassidim won’t rely on it – while the Litvishe will….
* Belz: accepted by many, but absolutely not accepted by anyone affiliated with the Edah.
* Agudah: per above, affiliated with Gur, generally seen as ‘less’ reliable.
Then there’s a couple of smaller hechsherim like Chasam Sofer Bnei Brak, Chug Chasam Sofer P”T, Rav Rubin, Beit Yosef…
Personally, having been previously affiliated with the Edah, I used to prefer their hechsher and, outside of Yerushalayim, Rav Landau (which the Edah-affiliated rabbonim generally allow for those affiliated with the Edah, but only outside of Yerushalayim).
But later, as I became a bit more open (like it or not), I came to realize that the ONLY issue involved is politics and ‘fake’ kashrus issues (ie, politicized semi-halachic issues), of the type of “we have a new chumrah and THEY don’t follow it as well, so THEY are a bad hechsher!”.
Thus, I used most of them. (Keeping in mind I don’t eat meat and fish – eliminating one major kashrus issue for me.) I really don’t believe the Belzer cheese (the blue one) or the Agudah cheese (the orange one) are somehow less kosher than the Edah cheese (the red one).
Life in Europe is great. Almost no hechsherim to choose from. Things are either kosher or not. Much better than this hechsherim-nonsense.