Live load all the way. When filling there are varying impacts & when emptying the flow pattern or system will affect the live load situation. As solid material encounters varying cross section the wall pressure varies considerably. Bin contents are also subject to seismic activities when the bin walls are disturbed.

There's a textbook for bin/silo design which is often mentioned in these forums & is also available from Amazon etc.

Fluid in tanks shouldn't be simplified to dead load either. When the pump starts up the material level fluctuates in a manner analogous to a conveyor belt tension. ■