if you mean metro trains {red m blue green, expo yes they wiill be on [mostly likely[ sunday/holiday schedule
if you mean metrolink Holiday Service Information
Limited train service is available on the days New Year's Day, Memorial Day, Independence Day, Labor Day, Thanksgiving Day and Christmas Day are observed.

If a holiday falls on a Saturday, it is usually observed on the previous Friday. If a holiday falls on a Sunday, it is usually observed on the following Monday.

Really depends on the train most longer distance routes don't have it, but the shorter distance trains like the Boston,NYC,Philly,Washington do, most of the trains in California do!!

Generally the bus is cheaper. That said, go to Amtrak and Greyhound websites for your particular trip and see what the prices are. If the train is close to the bus price take the train it's much nicer