Nanomechanical photothermal sensing has significantly advanced single-molecule/particle microscopy and spectroscopy, and infrared detection. In this approach, the nanomechanical resonator detects shifts in resonant frequency due to photothermal heating. However, the relationship between photothermal sensitivity, response time, and resonator design has not been fully explored. This paper compares three resonator types - strings, drumheads, and trampolines - to explore this relationship. Through theoretical modeling, experimental validation, and finite element method simulations, we find that strings offer the highest sensitivity (with a noise equivalent power of 280 fW/Hz