Miniature Joule-Thomson (J-T) cryocoolers are widely used in the cryogenic field due to their advantages of small size, and fast cooling. Selecting the appropriate refrigerant is a crucial task in designing a J-T cryocooler, as it significantly affects its cooling performance. To study the refrigerant-dependent influencing on the cryocooler's performance, an improved one-dimensional model for a conical double layer J-T cryocooler was developed. The model has been verified to have higher accuracy, faster computing speed, and applicability across a wider range of operating conditions. Nitrogen and argon, commonly used refrigerants with similar saturation temperatures, were investigated. Both simulation and experimental results indicate that argon exhibits a faster cooling rate, while nitrogen achieves a lower cooling temperature under the working conditions. The numerical studies suggest that argon's higher density and lower J-T coefficient contribute to its faster cooling characteristic, resulting in a higher heat transfer quantity in the double layer heat exchanger. However, increasing the vessel pressure can quickly reduce the difference in cooling rates between nitrogen and argon, and it may even make nitrogen more optimal. Moreover, it was observed that a significant portion of the cooling capacity is utilized to cool the cryocooler itself for both nitrogen and argon.