From my personal experience with (unfortunately) dark grey shutters facing south: Having just the holes open allows minimal airflow, which helps decrease the temperature between them and the window - because if the sun bakes the shutters, the air trapped behind them will get HOT - like hot enough that you can feel a difference when holding your hand against the glas.
For me it was better than having them completely closed, also it allowed a tiny bit of natural light in, but your mileage may vary