Since the late 1990s, sodium borohydride (NaBH₄, denoted SB) is presented as a promising hydrogen storage material and an attractive fuel (aqueous solution) of the direct fuel cell (or direct liquid-feed fuel cell). In 2007, the U.S. Department of Energy recommended a no-go for SB for vehicular applications and suggested work on ammonia borane (AB), another promising hydrogen storage material, which is also considered as a fuel for the direct fuel cell. Both boron hydrides in hydrogen and fuel cell applications are the topics of the present paper. The basics, issues, solutions to the issues and state-of-the-art are tackled but the discussion aims to compare the hydrides for either application. It is shown that there are many similarities between SB and AB in their features and applications. Nevertheless SB and AB as hydrogen storage materials do not compete. Rather, SB is intended more to portable technologies while AB to vehicular applications. Otherwise, when these hydrides are utilised as fuels of direct fuel cell, one question arises: what can be the advantage of developing the AB-powered fuel cell when it seems to be less effective, practical, and more complex than the SB-powered fuel cell? These aspects are discussed. However that may be, it is concluded that both SB and AB are not mature enough for the applications considered.