Deep Neural Networks (DNNs) are increasingly deployed across applications. However, ensuring their reliability remains a challenge, and in many situations, alternative models with similar functionality and accuracy are available. Traditional accuracy-based evaluations often fail to capture behavioral differences between models, especially with limited test datasets, making it difficult to select or combine models effectively. Differential testing addresses this by generating test inputs that expose discrepancies in DNN model behavior. However, existing approaches face significant limitations: many rely on model internals or are constrained by available seed inputs. To address these challenges, we propose DiffGAN, a black-box test image generation approach for differential testing of DNN models. DiffGAN leverages a Generative Adversarial Network (GAN) and the Non-dominated Sorting Genetic Algorithm II to generate diverse and valid triggering inputs that reveal behavioral discrepancies between models. DiffGAN employs two custom fitness functions, focusing on diversity and divergence, to guide the exploration of the GAN input space and identify discrepancies between models' outputs. By strategically searching this space, DiffGAN generates inputs with specific features that trigger differences in model behavior. DiffGAN is black-box, making it applicable in more situations. We evaluate DiffGAN on eight DNN model pairs trained on widely used image datasets. Our results show DiffGAN significantly outperforms a SOTA baseline, generating four times more triggering inputs, with greater diversity and validity, within the same budget. Additionally, the generated inputs improve the accuracy of a machine learning-based model selection mechanism, which selects the best-performing model based on input characteristics and can serve as a smart output voting mechanism when using alternative models.