The way I see it, Stormcloaks represent the colonists, and the Empire represents England. Yes, it would be better FOR ENGLAND if Skyrim remained under its control, but the people of Skyrim should be allowed to concern themselves with the fate of the people of Skyrim, not have to concern themselves with carrying the dead weight of the Empire.
Oh, and by the way, that doesn't mean I think Stormcloaks are some infallible heroes. Just as the colonists murdered tax collectors who were simply doing their job, the Stormcloaks have done some shady stuff too like murdering those who pledged allegiance to the Empire prior to large scale hostilities breaking out. I just think they're more in the right, because they have the right to decide what is best for themselves - they shouldn't have it dictated to them.
Unless I am meta-gaming the heck out of the game my character in-game would never know 90% of this stuff (the real facts).
My character didn't join the war until after the dragon menace was dealt with. Heck, he probably wouldn't have joined the war at all, since fighting only weakens both the Empire and Skyrim when the biggest threat to the free people of the world is the Thalmor. You can read the literature in game and come to that conclusion. Mostly just the desire to actually do the content is what pushed him over the edge though.