For discriminative models, metrics like accuracy, precision, recall, and F1-score matter most because these models focus on correctly classifying or predicting labels from input data.
For generative models, metrics that measure how well the model captures the data distribution are important. These include log-likelihood, perplexity, and Inception Score (for images). These metrics show how well the model can generate realistic new data.
In short, discriminative models are judged by how well they separate classes, while generative models are judged by how well they create or model data.