Which subatomic particle determines the identity of the element?

Protons

Explanation:

There are three major sub-automatic particles to consider here

1) Proton

2) Electrons

3) Nucleons

Two atom with same protons and electrons but different nucleons are called isotopes of the same element, hence the nucleon doesn't affect the identity of an element

Two atoms with same proton and nucleon but different electrons are usually a stable atom and an ion, both of the same elements, hence election number does not define the identity of the element

Two atoms with different proton numbers, no matter the electron and nucleon number will always be different elements