X-ray coronary angiography is a sub-optimal vascular imaging technique because it cannot suppress un-enhanced anatomy that may obscure the visualization of coronary arterydisease. The purpose of this paper is to evaluate the theoretical image quality of energy-resolved x-ray angiography (ERA) implemented with spectroscopic x-ray detectors (SXDs), which may overcome limitations of x-ray coronaryangiography. We modeled the large-area signal-difference-to-noise (SDNR) of contrast-enhanced vasculature in ERA images and compared with that of digital-subtraction angiography (DSA), which served as a gold standard vascular imaging technique. To this end, we used calibrated numerical models of the response of cadmium telluride SXDs including the effects of charge sharing, electronic noise, and energy thresholding. Our models assumed zero scatter, no pulse pile up and small signals such that image contrast is approximately linear in the area density of contrast agents. For DSA, we similarly modeled x-ray detection by cesium iodide energy-integrating detectors using validated numerical models. For ERA, we investigated iodine and gadolinium (Gd) contrast agents, two-material and three-material decompositions, analog charge summing for charge sharing correction, and optimized image quality with respect to the tube voltage and energy thresholds assuming cadmium telluride SXDs with three energybins. Our analysis reveals that a three-material decomposition using iodine contrast agents will require x-ray exposures that are approximately 400 times those of DSA to achieve the same SDNR as DSA in coronary applications, and is therefore not feasible in a clinical setting. However, three-material decompositions with Gd contrast agents have the potential to provide SDNR that is ∼45% of that of DSA for matched patient air kerma. For two-material decompositions that suppress soft-tissue, ERA has the potential to produce images with SDNR that is 50%-75% of that of DSA for matched patient air kermas but lower levels of tube loading. Achieving these SDNR levels will require the use of analog charge summing for charge sharing correction, which increased SDNR by up to a factor of 1.7 depending on the contrast agent and whether or not a two-material or three-material decomposition wasassumed. We conclude that three-material ERA implemented with Gd contrast agents and two-material ERA implemented with either iodine or Gd contrast agents, should be investigated as alternatives to DSA in situations where motion artifacts preclude the use of DSA, such as in coronaryimaging.