Which particle is most important to the identity of an atom?

There are three main types of particles in atoms: protons, neutrons, and electrons. Protons and neutrons are collectively referred to as "nucleons" because they both reside in the nucleus of the atom and possess a mass of approximately one unified atomic mass unit (or dalton).
Protons are stable particles in the nucleus of an atom. They have a positive charge of +1e and mass one dalton. They are considered a type of hadron and are composed of three quarks.
Neutrons are "neutral" or uncharged particles that also reside in the nucleus of an atom and have very slightly larger mass than protons. While a neutron is relatively stable in an atomic nucleus, it decays quickly outside an atomic nucleus.
Electrons are stable charged leptons (light atomic particles) that carry a negative charge and reside in a cloud orbiting the nucleus of an atom.
Because protons define the place of an atom in the periodic table (its "atomic number") as well as many of an atom's characteristics, they are considered the most important type of particle. Atoms with the same number of protons and a differing number of neutrons are considered "isotopes" of one another—for example, C-12 and C-14, isotopes of carbon that both have six protons. C-12 has six neutrons and C-14 eight neutrons, but both act identically in chemical reactions because they have the same number of protons.