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

Multiparameter quantum metrology in the Heisenberg Limit regime: many repetition scenario vs. full optimization