Allen wrenches have a very low chance of slipping out and damaging the furniture, even when you apply a lot of torque (in case it’s needed).
Philips screw are great for using an electric screwdriver.(side comment: most of the screws that people call Philips are actually Pozi, which is superior in all aspects. I only see Philips on super cheap stuff. Get a Pozi screwdriver, not a Philips one!)
Flat heads are just super cheap, but they are terrible for electric screwdrivers and if you slip you damage the furniture piece.
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