Clearly, there is no moral imperative on either side. The set of missions you perform are nearly identical. I'm pretty sure that the only way to get the nice, big house in Windhelm, Hjerim, is to finish the civil war one way or the other.
This has to do with an emotional connection. I think that most people like the rebel spirit, the anti-authority, and the freedom and independence minded Stormcloaks. I see that most people will start the game by following the Stormcloak guy out of Helgen. I did.
Once I started getting a sense of the racist, isolationist, xenophobic Nords I had a harder time supporting them. Ulfric it turns out, is just a little dictator in the making, using the Nords bigotry to further his ambitions. I could see that if Ulfric were High King all of Skyrim would be filled with racial ghettos like Windhelm. I may skip the civil war altogether when I start a new character, but I don't think I can ever support Ulfric, it just goes too much against my real-world sensibilities.
The deciding factor was when Thongcor Silver-Blood, in Markarth, launched a long rant on me blaming "you-people" for all the problems in Tamriel. I'm a Bosmer.
On a lighter note. After the Imperials win the war all the Jarls who supported Ulfric, and their staff, end up living in the Palace of the Kings in Windhelm. They sit around the big feasting table 24/7 just bitching and moaning about what they have lost. Believe me, they have nothing nice to say to me whenever I come in to talk to the new Jarl. Also, its been over a month in-game and Ulfric's body is still lying there. I finally just dragged his corpse up and laid him out in the middle of the table.
I was wondering, for those who fought for Skyrim's independence, do the Jarl's who sided with the Empire end up in Solitude just moping their lives away?