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Assuming that the shallow-decaying phase in the early X-ray light curves of gamma-ray bursts (GRBs) is attributed to the dipole radiations (DRs) of a newborn magnetar, we present a comparative analysis for the magnetars born in death of massive stars and merger of compact binaries with long and short GRB (lGRB and sGRB) data observed with the Swift mission. We show that the typical braking index (n) of the magnetars is ∼3 in the sGRB sample, and it is ∼4 for the magnetars in the lGRB sample. Selecting a sub-sample of the magnetars whose spin-down is dominated by DRs (n ≲ 3) and adopting a universal radiation efficiency of 0.3, we find that the typical magnetic field strength (B p ) is 1016 G versus 1015 G and the typical initial period (P 0) is ∼20 ms versus 2 ms for the magnetars in the sGRBs versus lGRBs. They follow the same relation between P 0 and the isotropic GRB energy as |$P_0\propto E_{\rm jet}^{-0.4}$|⁠. We also extend our comparison analysis to superluminous supernovae (SLSNe) and stable pulsars. Our results show that a magnetar born in merger of compact stars tends to have a stronger B p and a longer P 0 by about one order of magnitude than that born in collapse of massive stars. Its spin-down is dominated by the magnetic DRs as old pulsars, being due to its strong magnetic field strength, whereas the early spin-down of magnetars born in massive star collapse is governed by both the DRs and gravitational wave (GW) emission. A magnetar with a faster rotation speed should power a more energetic jet, being independent of its formation approach. [ABSTRACT FROM AUTHOR]