While I am not sure about the previously offered explanation for why, it is correct that some local offices are slower than others. I am not sure it is correct that the Mississauga office is slower than most. Historically, timelines for local offices have varied relative to one another. The only one I have noticed to be slower than most, more often, is Montreal. Mississauga has been, at times, among the faster-known offices and, at other times, among the slowest (the latter particularly during the peak of the fraud crack-down, the epicenter of which was in Mississauga itself).
While all applications are sent to Sydney, yes "to start with," the actual processing of the application is done in the local office. And timelines from one office to another vary.
The CPC in Sydney receives the application, screens it for completeness, loads the application formally into GCMS (thus putting the application into process), and initiates the referrals for background checks from RCMP and CSIS (those clearances to be sent to local office). It is also likely (although IRCC does not reveal much at all about this stage of internal processing) that triage screening for risk indicators is also done in Sydney before the application is transferred to the local office (this used to for sure be a step done in Sydney, but we have seen little indication of pre-test RQs coming out of Sydney in the last year so it is not certain that is still done in Sydney).
In any event, it is the local office which processes the application, reviews and assesses the applicant and the application, schedules the test and interview, and conducts any non-routine process triggered along the way. Scheduling for and administration of the oath also takes place in the local office.