  We contrast the transport properties (dc resistivity, Seebeck coefficient),
optical conductivity, spectral functions, dynamical magnetic susceptibility,
and the NMR $1/T_1$ spin-lattice relaxation rate of the repulsive and
attractive infinite-dimensional Hubbard models in the paramagnetic phase for a
generic band filling. The calculations are performed in a wide temperature
interval using the dynamical mean-field theory with the numerical
renormalization group as the impurity solver. The attractive case exhibits
significantly more complex temperature dependences which can be explained by
the behavior of the half-filled Hubbard model in external magnetic field with
constant magnetization, to which the attractive Hubbard model maps through the
partial particle-hole transformation. The resistivity is non-monotonous for
strongly attractive case: it peaks significantly above the MIR value at a
temperature $T_\mathrm{max}$ where the quasiparticle band disappears. For both
signs of $U$ we find particle-hole asymmetry in the self-energy at low
energies, but with the opposite kind of excitations having longer lifetime.
This leads to a strong suppression of the slope of the Seebeck coefficient in
the attractive case, rather than an enhancement as in the repulsive case. The
spin-lattice relaxation rate in the strongly attractive case has a
non-monotonic temperature dependence, thereby revealing the pairing
fluctuations.
