The recently introduced Tren Maya nominally connect many major cities in the Yucatan, Quintana Roo, Campeche and Chiapas. However in practice the advantages of the train over the traditional bus depends entirely on the length of the trip and the flexibility of the travelers.
The train obviously has the advantage of not getting slowed down by traffic or road accidents. it also has a faster top speed than the bus. Comfort wise you can easily walk around on the train and there is a snack-bar. However many of these theoretical advantages are negated in reality. First, the train rarely travels at it’s top speed and the advantage of avoiding traffic is mitigated to a large extent by having the stations located inconveniently far outside the cities. For journeys of 3 hours or less the bus is probably a better option. Taking into account overall travel time it is likely as quick as the train, has far more frequent departures and costs about half as much (at least for international travellers).
An example would be Mérida to Valladolid. Taking the train would involve a minimum of one hour on public transport to the station at Teya. You are supposed to be at the station about 20-30 minutes before the train departure so that can be added to the time. The actual train journey is pretty quick at a just a shade under two hours. At Valladolid there is a shuttle bus to take you into town and this takes on average about 30 minutes from arrival. Adding these up makes a trip of around four hours door to door.
In contrast the ADO terminal is close to downtown Merida and can be accessed from most parts of the city within 30 minutes. The bus trip is about 2 hours 45 minutes but the bus will take you directly into the centre of Valladolid. Overall the trip door to door is a little less than three and a half hours and the price is around half that of the train. Additionally the bus has departures very frequently throughout the day and night. Aside from the novelty value the train doesn’t really offer any advantage over the bus.
For longer trips, say to Cancun Airport or Palenque the train’s advantage are more apparent and four or more hours on a train is definitely more comfortable than that time on a bus.