Europe is finally entering a season of liberalisation in the long-distance rail passenger market, which takes the form of on-track competition among public and private operators. The paper provides a broad-scope comparison of relevant European markets, belonging to liberalised and non-liberalised countries, aiming to point out the patterns in terms of supply, competition model and prices. The paper is based on a sample of heterogeneous 69 city-pairs, analysed in two fourteen days periods in 2019 (May/June and November). All available modes are observed, collecting info on companies, frequency of services, and cheapest price. The analysis starts from a schematisation of different business models, based on literature. Then, using the database, we study the country's supply structure, size, and level of intermodal and intra-modal competition through HHIs. Prices are analysed in two steps: the average prices and the price dispersion, searching for their main determinants, including but not limited to competition. Results show that a higher competition level is not always corresponding to low prices, which are instead determined by many other factors such as size of market, demand, socio-economic characteristics, subsidies, production costs, speed advantage, strength of the incumbent, etc. The competition level, instead, directly influences the quality, the supplied capacity, and the price dispersion.