We report on a consistent comparison between techniques of quantum and classical machine learning applied to the classification of signal and background events for the Vector Boson Scattering processes, studied at the Large Hadron Collider installed at the CERN laboratory. Quan- tum machine learning algorithms based on variational quantum circuits are run on freely available quantum computing hardware, showing very good performances as compared to deep neural networks run on classical computing facilities. In particular, we show that such kind of quantum neural networks are able to correctly classify the signal with an Area Under the characteristic Curve (AUC) that is very close to the one obtained with the corresponding classical neural network, but employ- ing a much lower number of resources, as well as less variable data in the training set. Albeit giving a proof-of-principle demonstration with limited quantum computing resources, this work represents one of the first steps towards the use of near term and noisy quantum hardware for practical event classification in High Energy Physics experiments.