The magnetism of the double perovskite compounds La2-xSrxFeCoO6 (x=0,1,2) is contrasted using magnetization, neutron diffraction, and electron paramagnetic resonance with the support from density functional theory calculations. La2FeCoO6 is identified as a long-range ordered antiferromagnet displaying a near-room temperature transition at TN=270 K, accompanied by a low temperature structural phase transition at TS=200 K. The structural phase transformation at TS occurs from R3̄c at 300 K to Pnma at 200 K. The density functional theory calculations support an insulating noncompensated antiferromagnetic structure. The long-range ordered magnetism of La2FeCoO6 transforms to short-range glassy magnetism as La is replaced with Sr in the other two compounds. The magnetism of La2FeCoO6 is differentiated from the nonequilibrium glassy features of Sr2FeCoO6 and SrLaFeCoO6 using the cooling-and-heating-in-unequal-fields magnetization protocols. This contrasting magnetism in the La2-xSrxFeCoO6 series is evidenced in electron paramegnetic resonance studies. The electronic density of states estimated using the density functional theory calculations contrast the insulating feature of La2FeCoO6 from the metallic nature of Sr2FeCoO6. From the present suite of experimental and computational results on La2-xSrxFeCoO6, it emerges that the electronic degrees of freedom, along with antisite disorder, play an important role in controlling the magnetism observed in double perovskites. © 2019 American Physical Society.