We compare the use of LSTM-based and CNN-based character-level word embeddings in BiLSTM-CRF models to approach chemical and disease named entity recognition (NER) tasks. Empirical results over the BioCreative V CDR corpus show that the use of either type of character-level word embeddings in conjunction with the BiLSTM-CRF models leads to comparable state-of-the-art performance. However, the models using CNN-based character-level word embeddings have a computational performance advantage, increasing training time over word-based models by 25% while the LSTM-based character-level word embeddings more than double the required training time.