Modern machine learning techniques commonly rely on complex, high-dimensional embedding representations to capture underlying structure in the data and improve performance. In order to characterize model flaws and choose a desirable representation, model builders often need to compare across multiple embedding spaces, a challenging analytical task supported by few existing tools. We first interviewed nine embedding experts in a variety of fields to characterize the diverse challenges they face and techniques they use when analyzing embedding spaces. Informed by these perspectives, we developed a novel system called Emblaze that integrates embedding space comparison within a computational notebook environment. Emblaze uses an animated, interactive scatter plot with a novel Star Trail augmentation to enable visual comparison. It also employs novel neighborhood analysis and clustering procedures to dynamically suggest groups of points with interesting changes between spaces. Through a series of case studies with ML experts, we demonstrate how interactive comparison with Emblaze can help gain new insights into embedding space structure.