Well, there are several ways of answering this question.

Firstly the favoring of Germanicus over Tiberius was not at all towards a genral coup as Tacitus and others may ostensibly imply. The uprising was the army venting their long grievances against the rules and management of Augustus. For years Tiberius had been essentially the "good cop" to Augustus "bad cop" when the soldiers asked for bonuses, pay rises and shorter service terms. When Tiberius was Emperor he tries to shift to where he is the bad cop and Germanicus is the good cop, but the guard want to force Tiberius to live up to his promises. So the hailing of Germanicus is not real preference. This is especially clear because when Germanicus threatens to commit suicide a soldier called his bluff and offered his sharper sword.

The bigger longer impact is both Germanicus solution to ending the revolt and Tiberius response. Germanicus deduced that the soldiers wanted a bonus, and Germanicus sought to provide via war booty by going to re-conquer Germany. While Germanicus has some impressive campaigns and is loved by the people for this, Tiberius is a realist and knows that Rome cannot afford the long term "Romanization" of Germany and has Germanicus recalled. So long term Tiberius makes clear that the Elbe is the border for Western Roman Territory and that Rome will not conquer Germany.

Even longer and only inferring from a character perspective. Long term is that Germanicus parades his baby boy Caligula to help get his soldiers to go on his campaign. Now for a child's first memories to be being fawned over and loved by a mass of people that forms a lot to your psyche. How much is debatable but it probably sets in motion an acute awareness in this boy of his importance and the development of an ego.