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We have probed the crystalline electric-field ground states of pure |J=7/2,Jz=±5/2⟩ as well as the anisotropic c−f hybridization in both valence fluctuating systems α- and β-YbAlB4 by linear polarization dependence of angle-resolved core level photoemission spectroscopy. Interestingly, the small but distinct difference between α- and β-YbAlB4 was found in the polar angle dependence of linear dichroism, indicating the difference in the anisotropy of c−f hybridization, which may be a key to understanding a heavy Fermi liquid state in α-YbAlB4 and a quantum critical state in β-YbAlB4.