In the area of multi-domain speech recognition, research in the past focused on hybrid acoustic models to build cross-domain and domain-invariant speech recognition systems. In this paper, we empirically examine the difference in behavior between hybrid acoustic models and neural end-to-end systems when mixing acoustic training data from several domains. For these experiments we composed a multi-domain dataset from public sources, with the different domains in the corpus covering a wide variety of topics and acoustic conditions such as telephone conversations, lectures, read speech and broadcast news. We show that for the hybrid models, supplying additional training data from other domains with mismatched acoustic conditions does not increase the performance on specific domains. However, our end-to-end models optimized with sequence-based criterion generalize better than the hybrid models on diverse domains. In term of word-error-rate performance, our experimental acoustic-to-word and attention-based models trained on multi-domain dataset reach the performance of domain-specific long short-term memory (LSTM) hybrid models, thus resulting in multi-domain speech recognition systems that do not suffer in performance over domain specific ones. Moreover, the use of neural end-to-end models eliminates the need of domain-adapted language models during recognition, which is a great advantage when the input domain is unknown.