Rome2Rio can be handy for letting you know what type of transportation is available from Point A to Point B and where you might need to transfer (especially useful if you need to use more than one mode of transportation), but it definitely sometimes overlooks useful intercity buses, and I'm not sure it has all the info on commuter rail lines, either.
I don't use it for driving times (preferring ViaMichelin) or air travel (preferring Google Flights or Skyscanner). Specialty websites are just going to be more reliable, normally.
I find Rome2Rio extremely unreliable as to fares, frequencies and travel times for public ground transportation--trains and buses. I have the impression it used to be better, but it may just be that I know more now than I did when I first consulted Rome2Rio back around 2014.
If you know you need to take a train or a bus, it's safer and usually more efficient to go straight to the website of the rail or bus company. Knowing there are trains every 4 hours (What does that even mean? It's just some sort of average.) isn't helpful to me; I want to know the times of trains when I want to travel (mid-morning, usually). For buses I sometimes just Google bus City A to City B and go directly to the operating company's website, because that can be faster than drilling down through Rome2Rio to find the name of the bus company.
I wouldn't use Google for intercity travel times unless I was driving and wanted a second opinion, beyond what ViaMichelin says.
Within a city, Google can be helpful for public-transportation routing, but the website of the local public-transit authority will probably be more complete. I've never paid attention to how accurate Google is on travel time by bus and subway, and I noticed in Istanbul that it seemed to ignore the very handy funiculars. (I think CityMapper does, too.) Google usually calculates walking times at 20 minutes per mile, which is accurate enough for me unless footing is challenging or the terrain is hilly or full of steps in lieu of sidewalks. But I don't expect to make Google's walking times if I'm pulling my suitcase or am making photos along the way.