Err...yes, each alliance have its own campaign entirely all the way to lvl 50 (it's not like WoW where you only have starter zones and then "share" zones) . Once you finish the main alliance campaign you can then move over to the the other alliance's campaign and play that as lvl 50 -> VR levels (instead of lvl 1). During all this, you can't interact with your buddies if they're not in the same alliance.
I don't know if they improved this "flaw", but unlike WoW where everyone is in the same "phase" , in ESO you are always in your alliance's phase, and you can only see your own alliance..even if you are in another alliance area. The only place you mingle with the other alliances is that PvP map in the middle...
So i think it is quite important while you are leveling to pick an alliance where your friends are in.
At lvl 50 and dungeon runs, i'm not sure what the restrictions are there.
To put it another way, you WILL be playing all the aliances campaigns -eventually- . So it probably does not matter which one you start with, unless you don't plan to play much further than lv \l50 (then it is easier to create 3 chars and play each campaign from lvl1-50) . So there are a lvl 1-50 version of each campaign and a lvl 50+++ version of each campaign.