Timely evaluation of neurovasculature via CT angiography (CTA) is critical to the detection of pathology such as ischemic stroke. Cone-beam CTA (CBCT-A) systems provide potential advantages in the timely use at the point-of-care, although challenges of a relatively slow gantry rotation speed introduce tradeoffs among image quality, data consistency and data sparsity. This work describes and evaluates a new reconstruction-of-difference (RoD) approach that is robust to such challenges. A fast digital simulation framework was developed to test the performance of the RoD over standard reference reconstruction methods such as filtered back-projection (FBP) and penalized likelihood (PL) over a broad range of imaging conditions, grouped into three scenarios to test the trade-off between data consistency, data sparsity and peak contrast. Two experiments were also conducted using a CBCT prototype and an anthropomorphic neurovascular phantom to test the simulation findings in real data. Performance was evaluated primarily in terms of normalized root mean square error (NRMSE) in comparison to truth, with reconstruction parameters chosen to optimize performance in each case to ensure fair comparison. The RoD approach reduced NRMSE in reconstructed images by up to 50%-53% compared to FBP and up to 29%-31% compared to PL for each scenario. Scan protocols well suited to the RoD approach were identified that balance tradeoffs among data consistency, sparsity and peak contrast-for example, a CBCT-A scan with 128 projections acquired in 8.5 s over a 180° + fan angle half-scan for a time attenuation curve with ~8.5 s time-to-peak and 600 HU peak contrast. With imaging conditions such as the simulation scenarios of fixed data sparsity (i.e. varying levels of data consistency and peak contrast), the experiments confirmed the reduction of NRMSE by 34% and 17% compared to FBP and PL, respectively. The RoD approach demonstrated superior performance in 3D angiography compared to FBP and PL in all simulation and physical experiments, suggesting the possibility of CBCT-A on low-cost, mobile imaging platforms suitable to the point-of-care. The algorithm demonstrated accurate reconstruction with a high degree of robustness against data sparsity and inconsistency.