For me it varies by trip and this is on either an opafiets or omafiets with a very heavy duty rear rack. One bike has a front frame mounted rack with a square basket on it that works great for a lot of stuff. Being frame mounted avoids any impact on handling. Other bike has a wine crate on the rear rack. Not sure I have a preference between the two.
I have some Clarijs panniers that can go on either. Large ones can hold two bags of groceries on each side.
For real bulk cargo I use our bakfiets.