You were collateral, caught up in a stormcloak ambush. Sadly, the captain is too arrogant to care and orders your execution alongside them. If you do follow him, Hadvar tells you himself you should never have been there.
I need a woman like Jenassa. Spend a month away from home with a strange woman, come home to food, $2000 and sex, then leave.
Well considering I just crossed the border into Skyrim and have no clue what the hell a Stormcloak is... I'd probably stick with the Hadvar.
For all I know those "Stormcloaks" could be nothing more than bandits who'll later gut me for fun, enslave me, consider me "in their debt" for them "saving" me, or get me killed in some other manner later on.
Plus he seemed like a sympathetic man when listing off the prisoners, as well as being part of a well known faction, so there's a chance he could be reasoned with.... Unlike that jerk ass captain who wants heads to roll and bodies hit the floor.
May God have mercy on your soul... - The Preacher Because I sure as hell won't. - The Gunslinger