What are the primary factors that determine whether a volcano erupts explosively or relitivly quietly.

Chemical composition, temperature, viscosity

different chemicals in an erupting volcano's magma affects the temperature, which in turn affects the viscosity, which affects the eruption itself

for example, less silica content in the magma means lower temperature which means the lava cools down faster and hardens faster, which means the viscosity increases, which in turn results in relatively quiet explosion.