In Czechia, the track (much like the highways) is managed by a state corporation, while the trains themselves are partly state-owned, partly private.
From my 25 years of commuting experience, the results are decidedly mixed:
* the track-managing state corporation, Správa železnic, is a shitshow that causes a lot of unnecessary delays by just ignoring needs of passengers and cargo companies alike; true bureaucrats,
* the highway-managing state corporation, Ředitelství silnic a dálnic, is very well managed by the latest director (Mátl) and really kicked off many projects in last years, which is notable in a very NIMBY-friendly country like Czechia,
* the state-owned railway company, České dráhy, used to be terrible, but competition forced it into providing quite decent services within last 10 years or so.
* the two main private competitors, Leo Express and Regiojet, are now visibly cash-strapped (esp. Regiojet), so the overall level of service has stagnated for several years. High costs of traction electricity don't help either. As of today, there isn't really a qualitative difference between boarding state-owned or privately-owned trains.