It really depends on how many injuries there are, I think? Like, the clinic's probably best if there aren't too many injuries, but the Great Hall's a better option for a triage, for all the reasons Tavros mentioned. It also means that the clinic people might be able to get the people doing useful things to help out a bit if they need to.

Of course, this is coming from someone who has nothing to do with the clinic people normally, so take this with a grain of salt.