What decides the nature of emulsifying agents?
An emulsifier is a surfactant. A surfactant is characterized by the fact that its molecule has one or more hydrophilic parts and one or more hydrophobic parts. The ratio between the molar mass of the hydrophilic parts and the molar mass of the hydrophobic parts in the molecule is expressed by its HLB value (Hydrophilic-lipophilic balance).

Higher HLB means higher water solubility, and lower HLB means lower water solubility.

The emulsifier should have a certain solubility in the outer phase of the emulsion to be distributed in the emulsion.

An emulsifier for forming o/w-emulsions should have higher water solubility, that means higher HLB, and an emulsifier for forming w/o-emulsions should have lower water solubility (= higher oil solubility), that means lower HLB. The corresponding range of HLB is given in the Wikipedia artivle above.