The ability to drive efficient micromixing on a microfluidic platform is crucial for a wide range of lab-on-a-chip applications. Here, we investigate the ability of acoustic waves generated on different geometric surfaces (concave and convex) to enhance the micromixing efficiency in droplet acoustomicrofluidic systems, and, concomitantly, to reduce the power consumption in these devices for a given performance requirement. Quite counterintuitively, we observe that although the acoustic streaming velocity, which scaled inversely with the droplet size, tended to be generally lower (by approximately 45%) when the flow is generated by transducers with convex surfaces compared to those with concave surfaces, the mixing efficiency is disproportionately higher: compared to pure diffusional mixing in the absence of the acoustic forcing, the mixing efficiency due to the acoustically driven convection increased by up to 25% and 43% on these respective surfaces. As such, the mixing enhancement cannot simply be attributed to an increase in the convective flow arising from the acoustic forcing. Rather, we observe the mixing enhancement to be due to the stronger chaotic advection arising in the transducer with the convex surface due to its diverging acoustic field into the droplet.