Dual-energy (DE) imaging is a promising advanced application of flat-panel detectors (FPDs) with a potential host of applications ranging from thoracic and cardiac imaging to interventional procedures. The performance of FPD-based DE imaging systems is investigated in this work by incorporating the noise-power spectrum associated with overlying anatomical structures ("anatomical noise" modeled according to a 1/f characteristic) into descriptions of noise-equivalent quanta (NEQ) to yield the generalized NEQ (GNEQ). Signal and noise propagation in the DE imaging chain is modeled by cascaded systems analysis. A Fourier-based description of the imaging task is integrated with the GNEQ to yield a detectability index used as an objective function for optimizing DE image reconstruction, allocation of dose between low- and high-energy images, and selection of low- and high-kVp. Optimal reconstruction and acquisition parameters were found to depend on dose; for example, optimal kVp varied from [60/150] kVp at typical radiographic dose levels (approximately 0.5 mGy entrance surface dose, ESD) but increased to [90/150] kVp at high dose (ESD approximately 5.0 mGy). At very low dose (ESD approximately 0.05 mGy), detectability index indicates an optimal low-energy technique of 60 kVp but was largely insensitive to the choice of high-kVp in the range 120-150 kVp. Similarly, optimal dose allocation, defined as the ratio of low-energy ESD and the total ESD, varied from 0.2 to 0.4 over the range ESD=(0.05-5.0) mGy. Furthermore, two applications of the theoretical framework were explored: (i) the increase in detectability for DE imaging compared to conventional radiography; and (ii) the performance of single-shot vs double-shot DE imaging, wherein the latter is found to have a DQE approximately twice that of the former. Experimental and theoretical analysis of GNEQ and task-based detectability index provides a fundamental understanding of the factors governing DE imaging performance and offers a framework for system design and optimization.