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We perform benchmark calculations for the ionization potential and electronic affinity of atoms and small molecules using several semilocal exchange-correlation functionals of density-functional theory with improved asymptotic behavior. We are particularly interested in a new generalized-gradient approximation for exchange [Armiento and Kümmel, Phys. Rev. Lett.2013, 111, 036402] that provides an energy functional whose functional derivative yields a potential with better decay behavior. We find that it yields energies that are worse than traditional energy functionals and potentials that are less accurate than functionals that model directly the exchange-correlation potential. However, we find that this functional offers a excellent balance between the quality of the energy and of the potential and is therefore a good compromise for applications that require at the same time reasonable energies and good potentials.