BMW Assist is contracted out to Mondial Assistance and companies such as mine will attend to your broken down vehicle depending on the time of day and the fault. You may otherwise have a BMW branded vehicle (i.e. 5er Touring) attend instead.
Although our technicians will not be as proficient as a dealer mechanic, they do undergo regular training in terms of diagnosing faults and safe vehicle recovery.
With respect to response times, it is like any business with busy and quiet periods. Although we aim to get to all customers as quickly as possible, we do have to prioritise certain cases, for example motorway jobs over non-starters at home addresses.
BMW has worked with Mondial Assistance since the 1980s so I'm confident the service standards are comparable to other providers out there.