  We discuss the Heisenberg limit in the multiparameter metrology within two
different paradigms -- the one, where the measurement is repeated many times
(so the Cram\'er-Rao bound is guaranteed to be asymptotically saturable) and
the second one, where all the resources are allocated into one experimental
realization (analyzed with the mimimax approach). We investigate the potential
advantage of measuring all the parameter simultaneously compared to estimating
them individually, while spending the same total amount of resources. We show
that in general the existence of such an advantage, its magnitude and
conditions under which it occurs depends on which of the two paradigms has been
chosen. In particular, for the problem of magnetic field sensing using $N$
entangled spin-$1/2$, we show that the predictions based purely on the
Cram\'er-Rao formalism may be overly pessimistic in this matter -- the minimax
approach reveals the superiority of measuring all the parameters jointly
whereas the Cram\'er-Rao approach indicates lack of such an advantage.
