I see the Empire throughout the series, and how they always managed to keep Tamriel together. It was only the Whitegold Concordant which disrupted the Nord way of life. I had issues when first deciding a side, since I know the Empire has previously succeeded in keeping the world from falling apart with their regulations. However, they are an organization who is afraid to lose control, since they've been in control since they could remember.
However, the Stormcloaks vie for their freedom of worship, and I was taught that religion has always been a free realm to go where you please. Logically, I can see how a man couldn't be considered a God, and I don't get the same sense of wonder when I see the shrine of Talos, as I would if I saw, say, the Shrine of Meridia. Also, I'm not a Nord character, and I see how little trust the Nords give to potential allies. If you look into Tamriel's past, you see the Snow Elves have changed because of their lack of trust (yes, being betrayed by two different races can do that to you...) and I believe history has a chance to repeat itself.
With that said, I could logically help fight for someone who not only distrusts me, but also has a chance of changing the face of their own race several thousand years into the future. It's the lack of change that changes the true spirit of a person, so I fight for the Empire.