Both Amtrak and Greyhound have websites where you can look up the routes and the cost. I know Amtrak has some Family Compartments available. That might be a good choice depending on the distance.
Generally Greyhound bus tickets are cheaper than train tickets. However, since traveling with children, you might consider the extra cost of a train worth it for the added comfort.
If you can afford it, go with the train. Greyhounds can have long lay overs at their hubs, and there is less room to move on a bus versus a train. The train will be a bit pricier, but it will be a smaller headache.
