We use JWST Near-Infrared Spectrograph observations from the Cosmic Evolution Early Release survey, GLASS-JWST ERS (GLASS), and JWST Advanced Deep Extragalactic Survey to measure rest-frame optical emission-line ratios of 89 galaxies at z > 4. The stacked spectra of galaxies with and without a broad-line feature reveal a difference in the [O iii]λ 4364 and Hγ ratios. This motivated our investigation of the [O iii]λ4364/Hγ versus [Ne iii]/[O ii] diagram. We define two active galactic nucleus (AGN)/star formation (SF) classification lines based on 21,048 Sloan Digital Sky Survey galaxies at z ∼ 0. After applying a redshift correction to the AGN/SF lines, we find 69.2% of broad-line active galactic nuclei (BLAGN) continue to land in the AGN region of the diagnostic, largely due to the [Ne iii]/[O ii] ratio. However, 33.0% of non-BLAGN land is in the AGN region as well. The [O iii]λ4364/Hγ versus [Ne iii]/[O ii] diagram does not robustly separate BLAGN from non-broad-line galaxies at z > 4. This could be due to star-forming galaxies having harder ionization, or these galaxies contain a narrow line AGN, which are not accounted for. We further inspected galaxies without broad emission lines in each region of [O iii]λ4364/Hγ versus [Ne iii]/[O ii] diagram and found that they have slightly stronger C iii]λ1908 fluxes and equivalent width when landing in the BLAGN region. However, the cause of this higher ionization is unclear and may be revealed by observing UV lines.