Natural gas is basically methane, CH4, when you burn it you're making CO2 and H2O (water) and you get energy out from both these changes.
But coal is much nastier, not only is there nitrogen and sulfur in there (which are both going to produce poisonous gases you'll need to do something about) but the ratio of carbon to hydrogen is much worse so we produce far more CO2 for the same amount of energy production.
Shutting coal plants and building gas plants instead makes a big difference. Not enough of a difference to prevent catastrophic climate change, but a big step in the right direction compared to subsidising coal.
I'm unsure if its better from a storage point of view. Yes you can pile up coal in a field, but I'd prefer a tank of gas. And there should be infrastructure for storage left after households move away from gas heating.
I'm speaking from a UK POV, the model would seem to hold for Europe and North America at least.
But most countries seem to be shifting to gas away from coal in the short term, wouldn't gas generation be better for that kind of situation, ie if you have mothballed gas and coal generation, why keep the coal around?