What happens if I kill Imperial guards transporting a Stormcloak prisoner?

To add immersion to the game, Bethesda added a bunch of "world encounters" that do nothing other than to provide some flavor as you travel around.

Among a ton of other things, Imperials escorting a Stormcloak around the map is one of these random world encounters. You can ignore them or help the Stormcloak: it doesn't matter.

There's another chance to help a prisoner outside of finding a chance encounter on the world map:

When you first enter Solitude, there's a prisoner being set up for an execution. You're technically not expected to save him: it's just a flavor event to give some background to what Solitude is (an Imperial stronghold). But it is technically possible. You don't get anything other than a "thanks, bro!" for doing it.

Some advice with the part about guards attacking: The Whiterun guards attacked you because attacking Imperial soldiers--even those holding Stormcloak prisoners--is considered a crime, and a bounty is obtained. However, freeing the prisoner before attacking the Imperials--thereby causing them to attack you--incurs no bounty, because you're reacting in self-defense. Hope that helps!