Over the past years, cryptocurrencies have experienced a surge in popularity within the financial markets. As of today, besides being considered for investment purposes, they also serve as a widely accepted form of currency for everyday transactions. Due to the intricate characteristics of financial markets and their dependence on various factors to determine the prices of stocks and assets, the ability to predict such price is crucial to make investment choices, especially in terms of cryptocurrencies. In this work, a comparative analysis on the suitability of Deep Learning (DL) algorithms (effective for time series forecasting) in predicting the price of three cryptocurrencies (namely: Bitcoin, BTC; Ethereum, ETH; and Ripple, XRP) is assessed in terms of both short-term and long-term prediction accuracy. The results, evaluated using Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), and coefficient of determination (denoted as \(R^{2}\) ), reveal that: Transformer is generally more effective for short-term forecasts and also performs well for long-term predictions; Convolutional Neural Network-Recurrent Neural Network (CNN-RNN) demonstrates the lowest complexity in terms of number of Multiply and ACcumulate (MAC) operations; SimpleRNN has the fewest parameters and the smallest FLASH memory requirement. Overall, CNN-Gated Recurrent Unit (CNN-GRU) provides the best joint accuracy-complexity for predicting BTC and ETH prices, whereas CNN-RNN yields superior results for XRP price prediction.