The timely discovery and monitoring of fatigue cracks in steel structures is an important task in order to ensure structural integrity. However, off-the-shelf strain sensors are small and their deployment is too spatially localized to successfully locate new crack formation or growth within acceptable confidence. A solution is the use of large-area electronics capable of covering large surfaces. The authors have previously developed a sensing skin technology based on a soft elastomeric capacitor (SEC) that consists of a highly compliant, low-cost, and scalable strain gauge that transduces surface strain into a measurable change in capacitance. In prior work, the SEC was fabricated using three flat layers that formed a parallel plate capacitor. An improvement to that design has recently been proposed, in which the dielectric layer is textured using a corrugated pattern, and preliminary work showed a substantial improvement in sensing performance due to the added in-plane stiffness and decrease in the sensor’s transverse Poisson’s ratio. This paper extends preliminary work by studying the textured sensor’s capability to quantify and discover a fatigue crack, and to study the general sensing performance in terms of linearity, sensitivity, resolution, and accuracy. Four specific corrugation patterns are investigated: a symmetric grid, a diagonal diagrid, a reinforced diagrid, and a non-symmetric re-entrant hexagonal honeycomb (auxetic) pattern. Experimental results show that the use of a texture results in a significant increase in sensing performance, with auxetic and reinforced diagrid patterns outperforming the other patterns. In particular, the auxetic and reinforced diagrid patterns allowed the discovery of a 0.28 mm and 0.31 mm fatigue crack, compared to a 0.53 mm crack for the untextured SEC, and resulted in up to 106% increase in sensitivity, 113% in linearity, 319% in resolution, and 582% in accuracy, compared to untextured SECs.