The Gemara (Berachot 39b) explains that when eating bread, it is preferable to recite HaMotzi on a complete loaf of bread, rather than a piece. Furthermore, if one has the choice to recite HaMotzi on a slice of bread which is made out of wheat flour or on a whole loaf made of barley flour (which is considered inferior), it is preferable to do so on the whole loaf (source). Nevertheless, the Gemara records a disagreement in which wheat flour is considered preferable. As such, the Shulhan Aruch (Orah Haim 167:1) rules that in such a case, one should bring both types of bread together while making the blessing. Practically speaking, however, if one has different options available but prefers one type for health reasons, for example, one may make HaMotzi on whatever one prefers, even if it is not whole. Similarly, the Magen Avraham, (O.H. 211:1) rules that it is more honorable to make a blessing on a whole fruit than on sliced fruit. Nonetheless, Rabbi Shmuel Kellin (Mahatzit HaShekel, § 211) says that if one prefers sliced fruit, one should ideally make a blessing over both the whole and sliced fruit, so as to fulfill all opinions. Despite this opinion, the Mishna Berura (Sha’ar HaTziun O.H. 211:5) points out that one would not be expected to combine those fruit and that perhaps this combination only applies to bread. As such, if one wishes to eat both types of fruit, one should make the blessing on the whole fruit and can consume the sliced fruit afterwards. If, however, one specifically prefers to eat that fruit which is sliced, then one could make the blessing on that.
Another area of practical application for this Halacha is in restaurants, in which often, small pieces of bread are provided near the sink where Netilat Yadaim is performed. This is done in accordance with the Shulhan Aruch’s (Orah Haim 166:1) ruling that one should not wait longer than the time it takes to walk twenty-two cubits between Netilat Yadaim and HaMotzi. Therefore, if one has a whole piece of bread at one’s table, it is preferable to recite HaMotzi over that rather than on the pieces. Although there is a slightly longer delay to reach one’s table, one has in mind that one has yet to make a blessing over the breadand therefore it is not considered an interruption.
Summary: All things being equal, it is preferable to recite HaMotzi and HaEtz/HaAdama on whole bread and whole fruit, respectively.