The only differences are the route you take out of Helgen and the encounters there (side with Hadvar and you'll fight Stormcloaks, side with Ralof and you'll fight Imperials).

There are also slightly different rewards if you choose to follow them to Riverwood. Hadvar's uncle Alvor will give you free materials if you went with him whereas Ralof's sister Gerdur will let you stay at their house.

Both can be used for levelling- they're both invincible and never turn hostile.

Neither choice affects the Civil War Questline or any other quests.

It's also worth noting that neither Ralof nor the Stormcloaks tried to cut your head off. Just food for thought there...