simcha613 – Eida Haredis seems to be the most widely held of and from what I’ve seen the most common one you will see on packaged food from a store, however I can’t recall seeing their teudah on any restaurants (does anyone here know if they even give hashgacha for eateries?)
From what I’m aware some ashkenazim don’t eat sefardi hechsherim and vice versa because of different chumros and/or kulos between them in schitah, removing the gid hanseh, etc.
When I was in Yeshiva about 8 years ago there were some rabbanim who weren’t a big fan of Beit Yosef claiming they didn’t feel comfortable with how it was run. I countered that it had Rav Ovadia’s name behind it and the customary answer I always got was, “yeah but Rav Ovadia isn’t the one checking every chicken” I thought that was a pretty weak answer as Rav Rubin also isn’t checking every chicken if you know what I mean. When I was getting married I told a rav I was inviting who teaches people for smicha in issur v’heter that the wedding hall was under Beit Yosef in case he had a problem with it and he smiled and said, “I like my Beit Yosef with salt and pepper please!”