Accurate simulations of gas turbines’ dynamic performance are essential for improvements in their practical performance and advancements in sustainable energy production. This paper presents models with extremely accurate simulations for a real dual-fuel gas turbine using two state-of-the-art techniques of neural networks: the dynamic neural network and deep neural network. The dynamic neural network has been realized via a nonlinear autoregressive network with exogenous inputs (NARX) artificial neural network (ANN), and the deep neural network has been based on a convolutional neural network (CNN). The outputs selected for simulations are: the output power, the exhausted temperature and the turbine speed or system frequency, whereas the inputs are the natural gas (NG) control valve, the pilot gas control valve and the compressor variables. The data-sets have been prepared in three essential formats for the training and validation of the networks: normalized data, standardized data and SI units’ data. Rigorous effort has been carried out for wide-range trials regarding tweaking the network structures and hyper-parameters, which leads to highly satisfactory results for both models (overall, the minimum recorded MSE in the training of the MISO NARX was 6.2626 × 10−9 and the maximum MSE that was recorded for the MISO CNN was 2.9210 × 10−4, for more than 15 h of GT operation). The results have shown a comparable satisfactory performance for both dynamic NARX ANN and the CNN with a slight superiority of NARX. It can be newly argued that the dynamic ANN is better than the deep learning ANN for the time-based performance simulation of gas turbines (GTs).