Recently, MOTIVA staff participated in a discussion on LinkedIn about how to select an accreditation body to meet the needs of the laboratory staff member asking the question. See the discussion by clicking on this link.
Besides the obvious criterion (does this AB accredit for my scope?) there may be some other issues to consider. Accreditation is only formal recognition of the laboratory's demonstrated competence and if we were to order the things that were important to the lab in terms of demonstrating technical competence, that might focus the questions to the prospective ABs during discussions with them. Remember that the AB works for lab (EU Directive in Europe notwithstanding). They are a service provider to the lab.
Some laboratories are just looking for the piece of paper (certificate) and for them, the choice will always be based on time and money. But the person asking the original question implied they wanted more than that and were looking for something more from such a service provider.
For example, the lab may wish to ask how the AB will assess their estimations of uncertainty associated with the tests on the desired scope of accreditation. Each AB does it differently but lab really needs the technical rigour in this part of their assessment. As well, assessments that concentrate more on customer service (not a principle behind 17025) than the technical testing and calibration processes is less useful to the lab. It will not catch things the lab really needs to have caught.
A good AB will be able to tell the lab how many findings is typical for a laboratory of their size and with an equivalent number of tests on the scope. Lean towards the AB with the higher number. That indicates depth of assessment.
Ask the AB if it is necessary that top management participate in the opening or closing meetings. Lean towards the one that says it is not mandatory, but a good idea nonetheless. That AB is motivating the lab to involve top management in these two important (but relatively short) events without imposing a rule.
Finally, know that an AB is supposed to walk the talk. How can an AB ask a lab to shore up a QMS process with holes in it, if theirs has the same issues? For the lab, the standard is ISO/IEC 17025. For the AB it is ISO/IEC 17011. Ask about feedback (complaints and compliments) processes, their disputes and appeals processes, and if these are publicly available. Determine the level of transparency they provide.
Some of the things the lab will not know (until the actual assessment) are about the conduct of the assessors. People is people. Each one is different and, in order to maintain the integrity and credibility of an accreditation program, assessors must be passionate about their science. That passion, however, should not result in running over lab staff in the pursuit of the evidence (or not) of laboratory competence and conformance to requirements.
As well, good assessors do not offer personal opinions. Their job is to compare documented requirements with observed conditions and link the two with evidence. Opinions are not part of those types of discussions. (In reality - how can a person who is passionate about something not have opinions??) But good assessors will check that part of their approach.
When all is said and done, an assessment is really supposed to be "a technical discussion between technically competent peers about a list of things to do." A lab that experiences that is getting the "value added" aspect of an assessment. That AB understands that the accredited test and calibration reports carry their logo too. Providing the lab with accreditation enhances both organization's credibility, and that is what we all really want.