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The steady-state current (dc) characterization of high temperature superconducting (HTS) coils is a key role of its performance assessing. Due to the orientation dependence of the critical current density, Jc(B,θ), the magnetic field distribution of a given HTS coils depends on the shape of coils as well as the consistent tape applied. In the present paper, the dc characterizations of two HTS coils with same turns but different architectures are modeled by using the 3D finite element method. It is revealed that the engineering critical currents of both coils are subject to the end parts of coils. As the dc current is applied, the central magnetic field emerged is similar for both of them. As the dc current increases, the generated voltage for Coil A with an high aspect ratio of height to outer radius, is much lower than that of Coil B with a squashed shape, implying that Coil A gives rise to a higher toleration for applied current, and then a better performance for potential magnet.