Board Thread:Lore Discussion/@comment-26213507-20150715194939/@comment-26896471-20150908141949

On the Imperial questiline, Balgruuf sends his axe to Ulfric. Peace if he accepts it, war if he returns it. On the Stormcloak questline, Ulfric sends Balgruuf his axe, peace if he accepts, war if he returns it. Both return the axe. @Jauffre to accuse Ulfric under the pretext of returning the axe is absurd.

What you also seem to be forgetting is that in the Imperial questline, Tullius gives the Dragonborn a message to give to Balgruuf, triggering "Message to Whiterun". At that point your quest journal reads "I am to deliver a message to the Jarl of Whiterun it is time for him to pick a side". It is this letter which prompts Balgruuf to pick a side and deliver the axe. We can only assume it was an ultimatum. So in the Imperial questline, Tullius forces Balgruuf to choose, in the Stormcloak questline,  it is Ulfric.