Full-field identification methods are increasingly used to adequately identify constitutive parameters to describe the mechanical behavior of materials. This research investigates the more recently introduced, one-step method of Integrated Digital Image Correlation (IDIC) with respect to the most commonly used, two-step method of Finite Element Model Updating (FEMU), which uses a subset-based digital image correlation algorithm. To make the comparison as objective as possible, both methods are implemented in the most equivalent manner and use the same FE-model. Various virtual test-cases are studied to assess the performance of both methods when subjected to different error sources: (1) systematic errors, (2) poor initial guesses for the constitutive parameters, (3) image noise, (4) constitutive model errors, and (5) experimental errors. Results show that, despite the mathematical similarity of both methods, IDIC produces less erroneous and more reliable results than FEMU, particularly for more challenging test-cases exhibiting small displacements, complex kinematics, misalignment of the specimen, and image noise.