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Exoplanet observations are currently analysed with Bayesian retrieval techniques. Due to the computational load of the models used, a compromise is needed between model complexity and computing time. Analysis of data from future facilities, will need more complex models which will increase the computational load of retrievals, prompting the search for a faster approach for interpreting exoplanet observations. Our goal is to compare machine learning retrievals of exoplanet transmission spectra with nested sampling, and understand if machine learning can be as reliable as Bayesian retrievals for a statistically significant sample of spectra while being orders of magnitude faster. We generate grids of synthetic transmission spectra and their corresponding planetary and atmospheric parameters, one using free chemistry models, and the other using equilibrium chemistry models. Each grid is subsequently rebinned to simulate both HST/WFC3 and JWST/NIRSpec observations, yielding four datasets in total. Convolutional neural networks (CNNs) are trained with each of the datasets. We perform retrievals on a 1,000 simulated observations for each combination of model type and instrument with nested sampling and machine learning. We also use both methods to perform retrievals on real WFC3 transmission spectra. Finally, we test how robust machine learning and nested sampling are against incorrect assumptions in our models. CNNs reach a lower coefficient of determination between predicted and true values of the parameters. Nested sampling underestimates the uncertainty in ~8% of retrievals, whereas CNNs estimate them correctly. For real WFC3 observations, nested sampling and machine learning agree within $2σ$ for ~86% of spectra. When doing retrievals with incorrect assumptions, nested sampling underestimates the uncertainty in ~12% to ~41% of cases, whereas this is always below ~10% for the CNN.