In this paper, we present a comparative study on the robustness of two different online streaming speech recognition models: Monotonic Chunkwise Attention (MoChA) and Recurrent Neural Network-Transducer (RNN-T). We explore three recently proposed data augmentation techniques, namely, multi-conditioned training using an acoustic simulator, Vocal Tract Length Perturbation (VTLP) for speaker variability, and SpecAugment. Experimental results show that unidirectional models are in general more sensitive to noisy examples in the training set. It is observed that the final performance of the model depends on the proportion of training examples processed by data augmentation techniques. MoChA models generally perform better than RNN-T models. However, we observe that training of MoChA models seems to be more sensitive to various factors such as the characteristics of training sets and the incorporation of additional augmentations techniques. On the other hand, RNN-T models perform better than MoChA models in terms of latency, inference time, and the stability of training. Additionally, RNN-T models are generally more robust against noise and reverberation. All these advantages make RNN-T models a better choice for streaming on-device speech recognition compared to MoChA models.