Speech embeddings are fixed-size acoustic representations of variable-length speech sequences. They are increasingly used for a variety of tasks ranging from information retrieval to un-supervised term discovery and speech segmentation. However, there is currently no clear methodology to compare or optimize the quality of these embeddings in a task-neutral way. Here, we systematically compare two popular metrics, ABX discrimination and Mean Average Precision (MAP), on 5 languages across 17 embedding methods, ranging from supervised to fully unsu-pervised, and using different loss functions (autoencoders, cor-respondance autoencoders, siamese). Then we use the ABX and MAP to predict performances on a new downstream task: the unsupervised estimation of the frequencies of speech segments in a given corpus. We find that overall, ABX and MAP correlate with one another and with frequency estimation. However, substantial discrepancies appear in the fine-grained distinctions across languages and/or embedding methods. This makes it un-realistic at present to propose a task-independent silver bullet method for computing the intrinsic quality of speech embed-dings. There is a need for more detailed analysis of the metrics currently used to evaluate such embeddings.