Purpose: Timely detection of neurovascular pathology such as ischemic stroke is essential to effective treatment, and systems for cone-beam CT (CBCT) could provide CT angiography (CTA) assessment in a timely manner close to the point of care. CBCT systems suffer from slow rotation speed and readout speed, which leads to inconsistent or sparse dataset. This work describes a new reconstruction method using a reconstruction of difference (RoD) approach that is robust against such factors. Methods: Important aspects of CBCT angiography were investigated, weighting tradeoffs among the magnitude of iodine enhancement (peak contrast), the degree of data consistency, and the degree of data sparsity. Simulation studies were performed across a range of CBCT half-scan acquisition speed ranging ∼3 - 17 s. Experiments were conducted using a CBCT prototype and an anthropomorphic neurovascular phantom incorporating a vessel with contrast injection with a time-attenuation (TAC) injection giving low data consistency but high peak contrast. Images were reconstructed using filtered back-projection (FBP), penalized likelihood (PL), and the RoD algorithm. Data were evaluated in terms of root mean square error (RMSE) in image enhancement as well as overall image noise and artifact. Results: Feasibility was demonstrated for 3D angiographic assessment in CBCT images acquired across a range of data consistency and sparsity. Compared to FBP, the RoD method reduced the RMSE in reconstructed images by 50.0% in simulation studies (fixed peak contrast; variable data consistency and sparsity). The improvement in RMSE compared to PL reconstruction was 28.8%. The phantom experiments investigated conditions of low data consistency, RoD provided a 15.6% reduction in RMSE compared to FBP and a 16.3% reduction compared to PL, showing the feasibility of RoD method for slow-rotating CBCT-A system. Conclusions: Simulations and phantom experiments show the feasibility and improved performance of the RoD approach compared to FBP and PL reconstruction, enabling 3D neuro-angiography on a slowly rotating CBCT system (e.g., 17.1s for a half-scan). The algorithm is relatively robust against data sparsity and is sensitive in detecting low levels of contrast enhancement from the baseline (mask) scan. Tradeoffs among peak contrast, data consistency, and data sparsity are demonstrated clearly in each experiment and help to guide the development of optimal contrast injection protocols for future preclinical and clinical studies.