Echo States Networks (ESN) and Long-Short Term Memory networks (LSTM) are two popular architectures of Recurrent Neural Networks (RNN) to solve machine learning task involving sequential data. However, little have been done to compare their performances and their internal mechanisms on a common task. In this work, we trained ESNs and LSTMs on a Cross-Situationnal Learning (CSL) task. This task aims at modelling how infants learn language: they create associations between words and visual stimuli in order to extract meaning from words and sentences. The results are of three kinds: performance comparison, internal dynamics analyses and visualization of latent space. (1) We found that both models were able to successfully learn the task: the LSTM reached the lowest error for the basic corpus, but the ESN was quicker to train. Furthermore, the ESN was able to outperform LSTMs on datasets more challenging without any further tuning needed. (2) We also conducted an analysis of the internal units activations of LSTMs and ESNs. Despite the deep differences between both models (trained or fixed internal weights), we were able to uncover similar inner mechanisms: both put emphasis on the units encoding aspects of the sentence structure. (3) Moreover, we present Recurrent States Space Visualisations (RSSviz), a method to visualize the structure of latent state space of RNNs, based on dimension reduction (using UMAP). This technique enables us to observe a fractal embedding of sequences in the LSTM. RSSviz is also useful for the analysis of ESNs (i) to spot difficult examples and (ii) to generate animated plots showing the evolution of activations across learning stages. Finally, we explore qualitatively how the RSSviz could provide an intuitive visualisation to understand the influence of hyperparameters on the reservoir dynamics prior to ESN training.