Variation in speech is often quantified by comparing phonetic transcriptions of the same utterance. However, manually transcribing speech is time-consuming and error prone. As an alternative, therefore, we investigate the extraction of acoustic embeddings from several self-supervised neural models. We use these representations to compute word-based pronunciation differences between non-native and native speakers of English, and between Norwegian dialect speakers. For comparison with several earlier studies, we evaluate how well these differences match human perception by comparing them with available human judgements of similarity. We show that speech representations extracted from a specific type of neural model (i.e. Transformers) lead to a better match with human perception than two earlier approaches on the basis of phonetic transcriptions and MFCC-based acoustic features. We furthermore find that features from the neural models can generally best be extracted from one of the middle hidden layers than from the final layer. We also demonstrate that neural speech representations not only capture segmental differences, but also intonational and durational differences that cannot adequately be represented by a set of discrete symbols used in phonetic transcriptions.