We construct spin-improved holographic light-front wavefunctions for the nucleons (viewed as quark-diquark systems) and use them to successfully predict their electromagnetic Sachs form factors, their electromagnetic charge radii, as well as the axial form factor, charge and radius of the proton. The confinement scale is the universal mass scale of light-front holography, previously extracted from spectroscopic data for light hadrons. With the Dirac and Pauli form factors normalized using the quark counting rules and the measured anomalous magnetic moments respectively, the masses of the quark and diquark are the only remaining adjustable parameters. We fix them using the data set for the protons Dirac-to-Pauli form factor ratio, and then predict all other data without any further adjustments of parameters. Agreement with data at low momentum-transfer is excellent. Our findings support the idea that light (pseudoscalar and vector) mesons and the nucleons share a non-perturbative universal holographic light-front wavefunction which is modified differently by their spin structures.