Tri-Star or UDA is the best there is - They only get the COA if the Auto is signed in the presense of a Tri-Start or UDA rep.
Steiner or MM authenticate based on how the Auto looks compared to other Auto's -i.e. If you had a TB auto Jersey and you got it from someone with NO COA you could take it to them and they would Authenticate it, while I know they are good at what they do - There is a large margin for error there.
They are at many Auto sessions with Players and authenticate that way as well, but most of what they do is based on people bring items to them for Authentication.
FYI -Randy has his OWN hologram that he has put on anything he signs (at auto sessions) - So if it's a Randy auto and they said it came from a session, make sure it has the official Randy Moss Holo along with the Holo of the people putting on the signing. He has not ALWAYS done that, but as long as he's been a Patriot he has had that second Holo - So anything with Randy Sig. on a Patriot Jersey/Hat/Football/Helmet/Etc would have it.
Another good one for Authenication is Gridiron Legends / GRIDIRON AUTHENTICS - They do Photo COA's with their Numbered Holo - and are genuine - They have a lot of Patriot's under contract and do a lot of Signings.