Compressing large language models (LLMs), often consisting of billions of parameters, provides faster inference, smaller memory footprints, and enables local deployment. Two fundamental compression techniques are pruning and quantization, with the former eliminating redundant connections in model layers and the latter representing model parameters with as few as 4 bits. The key tradeoff is between the degree of compression and the impact on the quality of the compressed model. Existing research on LLM compression primarily focuses on performance in terms of general metrics like perplexity or downstream task accuracy. More fine-grained metrics, such as those measuring parametric knowledge, remain significantly underexplored. To help bridge this gap, we present a comprehensive analysis across multiple model families (ENCODER, ENCODER-DECODER, and DECODER) using the LAMA and LM-HARNESS benchmarks in order to systematically quantify the effect of commonly employed compression techniques on model performance. A particular focus is on tradeoffs involving parametric knowledge, with the goal of providing practitioners with practical insights to make informed decisions on compression. All of our code and checkpoints will be released.