Checkrides can be performed under part 61 or 141 by:
FAA Inspector: An FAA employee (based at the local FSDO) who performs checkrides. There is no charge, but it must be scheduled far in advance and may be cancelled on short notice, as it is subject the the availability on an inspector.
DPEs (Designated Pilot Examiners): A private individual (non-FAA) who is trained and designated by the FAA to perform checkrides. The DPE is paid a fee by the applicant for his time.
At a part 141 school, there is also an option to have a staff member who is designated as having examining authority... essentially that staff member is like a DPE, but is only authorized to do checkrides for that school's 141 program. Typically the examiner would also be a chief pilot. Not all 141 schools have examining authority, the ones that don't use DPEs and/or FAA inspectors for checkrides.
So the question you want to ask is if the school has examining authority. There is a benefit to that, in that you will know the staff, and they will know you so it takes some stress and uncertainty out of the checkride process. Your primary instructor(s) will not be the examiner, that's not allowed (although you may have received some instruction from the examiner along the way).