ComboBox supports a cellFactory which allows essentially an arbitrary UI for displaying the item in each cell. ChoiceBox does not have this functionality and will only display text in each cell (which you can configure using a converter).
See http://docs.oracle.com/javase/8/javafx/user-interface-tutorial/combo-box.htm#BABJCCIB listing 16.5 for an example of a custom cell factory in a combo box.