Cations, having positive charges, have higher IEs than their neutral elements. Attribute to the fact that while the nuclei have the same positive charge, while the number of electrons diminish in the cation, creating less electron-electron repulsion, and greater Zeff. You can refer to charts showing I1, I2, etc., and the numbers beyond I1 (equivalent to the IE of cations) are much greater than that of I1 (the IE of the neutral element).
Anions have the same positive charge as their parent elements, but have extra electrons. Removing an electron is not as difficult, considering anions are larger than the neutral elements and are less tightly bound. Also, the Electron Affinity of an element is - the IE of the reverse reaction, the anion going to the neutral element. Charts show the values of EA are much smaller than for IE of elements, so we conclude
IE cation > IE neutral > IE anion.