Not so much a direct question, more of an opinion needed! In the quest 'the jagged crown', once the crown is retreived, you are to take it back to Urflich Stormcloak (or alternativly General Tullius depending on who you followed on escaping from Helgen [THIS IS NOT THE CHOICE IN QUESTION]) and join the stormcloaks (or Imperials). However, "only" on doing my internet research did I find out that you can betray whomever you are to take it back to (General Tullius of the Imperials or Urflich Stormcloak).... at NO point does it tell you that you have a choice during the actual gameplay. OR DOES IT!? Because if it does then ive totally missed it, but if it doesnt then is it just me or is that a HUGE gap in game? Regardless of if you as a Skyrim player like to visit all the cities on their own by walking across the land, or follow the main quests to get to the cities (i have done both), i still think the game should tell you about that choice when it comes along, not finding out by chance. Cheers people
AFAIK there is no indication in the game that you can switch sides at that point by taking the Crown to the leader of the other faction.
However it should be noted that who you follow out of Helgen has no bearing at all on which side you choose, either at first or when you turn in the Crown. You can follow Ralof out and still join the Legion, you can follow Hadvar out and still join the Stormcloaks. The fact that each one gives you an objective about joining his own side is irrelevant.