Deep learning (DL)-based attenuation correction (AC) is promising to improve myocardial perfusion (MP) SPECT. We aimed to optimize and compare the DL-based direct and indirect AC methods, with and without SPECT and CT mismatch. One hundred patients with different 99mTc-sestamibi activity distributions and anatomical variations were simulated by a population of XCAT phantoms. Additionally, 34 patients 99mTc-sestamibi stress/rest SPECT/CT scans were retrospectively recruited. Projections were reconstructed by OS-EM method with or without AC. Mismatch between SPECT and CT images was modeled. A 3D conditional generative adversarial network (cGAN) was optimized for two DL-based AC methods: (i) indirect approach, i.e., non-attenuation corrected (NAC) SPECT paired with the corresponding attenuation map for training. The projections were reconstructed with the DL-generated attenuation map for AC; (ii) direct approach, i.e., NAC SPECT paired with the corresponding AC SPECT for training to perform direct AC. Mismatch between SPECT and CT degraded DL-based AC performance. The indirect approach is superior to direct approach for various physical and clinical indices, even with mismatch modeled. DL-based estimation of attenuation map for AC is superior and more robust to direct generation of AC SPECT.