In [GT], Gan and Takeda prove the local Langlands conjecture for GSp₄. In [GTan], Gan and Tantano prove the local Langlands conjecture for GU₂(D), the inner form of GSp₄. Under these parametrizations, the L-packets L_\ [phi]{GT} attached to a parameter $\phi$ do not give an explicit realization of supercuspidal representations as compactly induced from open compact mod center subgroups. For tame regular discrete L-parameters [phi] of GSp₄ and its inner form, we extend the construction of DeBacker and Reeder given in [DR] to attach L-packets \$L_\phi[DR] of depth-zero compactly induced supercuspidal representations. We then show that the two parametrizations agree, namely for tame regular discrete L -parameters [phi], we have L_\[phi][GT]=L_\[phi][DR]