Low-temperature ultrahigh-resolution photoemission (PE) spectroscopy of the recently discovered binary icosahedral (i) Cd5.7Yb and its 1/1-cubic approximant Cd6Yb has commonly revealed a sharp Fermi edge with a marked spectral intensity decrease towards the Fermi level (EF), indicating the presence of a dip near EF which is consistent with the recent result of electronic structure calculations [Y. Ishii and T. Fujiwara, Phys. Rev. Lett. 87, 206408 (2001)], and the dip at EF is found to be much deeper in i-Cd5.7Yb than in 1/1-Cd6Yb. Moreover, surface core-level shifts (SCS's) are clearly observed in the quasicrystal and the approximant, and the SCS's are found to be substantially different between these two compounds of different long-range orders.