The main bone of contention is with detection. The reasoning goes that, if sprinkler systems are reliant on heat to activate, the action of smoke ventilators could delay this process. The same contention works the other way around: local effects of the sprinkler spray and its cooling effects on nearby natural ventilators can reduce the capacity of removing smoke out of those ventilators.
Some also point to the availability of oxygen caused by a smoke ventilation system’s inlet air function negating the effectiveness of the sprinkler setup. However testing in the USA some years ago revealed these to be non-issues in most situations. It is true that inlet vents will provide more oxygen to the fire which could cause it to remain alive and possibly spread elsewhere, although its spread will be limited due to reduced temperatures and radiation levels (removing smoke = removing heat).
However, with the presence of the sprinklers, as they are triggered by a rise in temperature, typically only the sprinkler closest to the fire will activate. From NFPA journal statistics, roughly 85% of the time, when there’s a fire, just one sprinkler operates.