Comparing two (large) language models (LMs) side-by-side and pinpointing their prediction similarities and differences on the same set of inputs are crucial in many real-world scenarios, e.g., one can test if a licensed model was potentially plagiarized by another. Traditional analysis compares the LMs' outputs on some benchmark datasets, which only cover a limited number of inputs of designed perspectives for the intended applications. The benchmark datasets cannot prepare data to cover the test cases from unforeseen perspectives which can help us understand differences between models unbiasedly. In this paper, we propose a new model comparative analysis setting that considers a large input space where brute-force enumeration would be infeasible. The input space can be simply defined as all token sequences that a LM would produce low perplexity on -- we follow this definition in the paper as it would produce the most human-understandable inputs. We propose a novel framework \our that uses text generation by sampling and deweights the histogram of sampling statistics to estimate prediction differences between two LMs in this input space efficiently and unbiasedly. Our method achieves this by drawing and counting the inputs at each prediction difference value in negative log-likelihood. Experiments reveal for the first time the quantitative prediction differences between LMs in a large input space, potentially facilitating the model analysis for applications such as model plagiarism.