It is decided by the manufacturer. Engines 1-4 are the green system on the Airbus 340, and from this, normal brakes work and nose wheel steering, but not parking brake, this is engine 2 blue system, which is not running.
Outboard engines also provide more torque for a turn, making a tighter turn a little easier with less thrust when compared to an inboard engine, I suppose.
A330 has a green hydraulic system working with both engines 1-2, so either maybe shut down.
B777, either engine can be shut down and the same for my B787-9. Either engine.
Many conditions are to be considered before single engine taxi, and supplementary techniques and checklists need to be followed. You must think ahead and not all airports allow "reduced engine taxi", is the technical term!