You do occasionally get more information in an administration file than the usual bare minimum. I seem to remember coming across one in my wife's family where the administrator had failed to deal with the estate in the time laid down, so there was a record of the court's deliberations and probably a few extra family names. In other cases there might be some dispute as to who would be responsible for the administration, so again, a bigger file than usual.
I don't know much about Chancery cases other than that this is where probate disputes ended up, but I would expect the court records to include at least a bit of background. That is probably going to be your best guide as to how useful the administration file will be. However, the only sure way to find out would be to order a copy or to go to York and look at the original.
Arthur