We report the first direct frequency comparison between two multi-ion optical clocks based on the S${}_{1/2}$ to D${}_{5/2}$ transition in Ca${}^{+}$ and Sr${}^{+}$ ions. Using linear chains of up to nine Ca${}^{+}$ ions and six Sr${}^{+}$ ions, we demonstrate improved stability as a function of the number of ions that are contributing to the laser frequency stabilization servo. The measured joint fractional frequency stability of the two clocks reaches $1.37(12)\times {10}^{-15}$ at one second, placing an upper bound on the same stability of one of the clocks at $9.6(8)\times {10}^{-16}$ in one second. We measured the frequency ratio of the two clocks, with a relative uncertainty of $2\times {10}^{-17}$, to be $R_{\mathrm{\text{Sr/Ca}}}=1.08207653638189698(2)$, where the systematic uncertainty is primarily limited by the room-temperature blackbody radiation. Our direct measurement represents an order of magnitude improvement compared to existing indirect frequency ratio measurements. Furthermore, by combining our results with recent absolute frequency measurements of the transition, referenced to a primary frequency standard, we refined the absolute frequency of the Ca${}^{+}$ transition to ${\nu }_{{\mathrm{\text{Ca}}}^{+}}=411042129776400.21(4)$ Hz, reducing its uncertainty by a factor of three. This study presents the first direct comparison between two multi-ion optical clocks, highlighting their significant potential for future applications in fundamental physics tests, geodesy, and precision metrology.