I guess this is a pretty subjective discussion. If you are talking about a specific field of authenticating your ranking falls apart. In the modern celebrity category JSA and Global would be tied for worst.
According to his profile, Ed collects:
Sports, History/Politics, Classic Hollywood and Stage, Music.
Global is a complete wasteland as far as authentication. JSA and PSA seem to have been in significant decline for some time, while the glowing early reviews of Beckett seem to have been pretty quickly countered by significant concerns cited on this forum. I don't like any of them.
Google "JSA PSA Hauls of Shame" for a number of their "best" mistakes. My favorites are the Andre the Giant facsimile signature on a magazine that was authenticated or the Clem Labine signed baseball authenticated as "Ernie Davis" or perhaps James Earl Ray signed index authenticated as James Earl Jones. There are so many of them yet they still seem to be held in such high esteem. I'd rather take the word of you guys on this forum!
The sad thing is, eBay believes these guys.
An affiliate of mine listed some products which eBay then deleted because they never came with COA's from their approved authenticators. Only thing is, all their approve authenticators are sports authenticators and don't know much about music.
One item came with a COA from JSA which they also removed, so one minute they trust their approved and then next minute they delete an item authenticated by them.
They really need someone who knows music to authenticate for them.