We theoretically study plasmonic antennas featuring areas of extremely concentrated electric or magnetic field, known as hot spots. We combine two types of electric-magnetic complementarity to increase the degree of freedom for the design of the antennas: bowtie and diabolo duality and Babinet's principle. We evaluate the figures of merit for different plasmon-enhanced optical spectroscopy methods and optical trapping: field enhancement, decay rate enhancement, quality factor of the plasmon resonances, and trapping potential depth. The role of Babinet's principle in interchanging electric and magnetic field hot spots and its consequences for practical antenna design are discussed. In particular, diabolo antennas exhibit slightly better performance than bowties in terms of larger field enhancement and larger Q factor. For specific resonance frequency, diabolo antennas are considerably smaller than bowties, which makes them favorable for the integration into more complex devices but also makes their fabrication more demanding in terms of spatial resolution. Finally, we propose a Babinet-type dimer antenna featuring electromagnetic hot spot with both the electric and magnetic field components treated on an equal footing.