Machine learning and deep learning-based neural networks have gained a lot of attention, in recent times, in the field of time series data forecasting. The major reason behind this is their superiority over traditional methods toward capturing the trend, seasonality, and other long as well as short-term dependencies present in the time series data. Accurate prediction of electricity prices is extremely crucial in the decision-making process for electrical market operators and other related stakeholders for security, reliability, and maximum profitability. This paper, first, identifies the need for comparing various short-term forecasting techniques on a common electrical market so that transparent conclusions on common ground can be made regarding selection of suitable forecasting technique and then provides a sophisticated comparative analysis in terms of prediction performances and computational time needed for training the models on input historical price data. The study presents detailed insights on most trending deep learning-based data-driven forecasting approaches used in short-term price forecasting (STPF), including variants of Long Short-Term Memory (LSTM), Convolutional Neural Network (CNN), and hybrid CNN-LSTM models in context of forecasting electricity prices for day-ahead market. Stacked LSTM is observed to outperform others in the considered study as Root Mean Square Error (RMSE) got reduced by 17.6% and a reduction of 41.3% is observed in Mean Absolute Error (MAE) as compared to that of classic LSTM model, whereas CNN is established to be the fastest model to train.