There are many differences between choosing to ally with the Empire and choosing to ally with the Rebel Alliance. If you join the Rebel Alliance, then you’ll be able to build a hero command immediately, and you’ll have to wait until Headquarters level 4 to build the Factory. If you join the Empire, you’ll be able to build the Factory immediately, but you will have to wait to build the Hero Command until HQ level 4.
Also, you’ll have completely different troops for each side, with different health and attack statistics. Each barrack contains 8 possible troop types. You have the weak generalist (Stormtrooper/Rebel Soldier), your turret attacker (Wookiee Warrior or Phase II Dark Trooper), your wall crusher (Bantha Rider/Dewback Trooper), and your resource looting troop (Rebel Pathfinder/Scout Trooper).
Next you have your healer (Medic Droid/Repair Droid), your machine gunner (Heavy Soldier/Heavy Stormtrooper), and your long range striker (Rebel Sharpshooter/Sniper Trooper). Then you have the special troops (Rebel Vanguard/Shock Trooper) that do splash damage, and oddly enough, are the only pair of troops with similar stats.
Rebel troops are generally much stronger per troop type than empire troops are. If you’re in the empire you get an advantage to mitigate this which is the ability to build a second Unit Transport immediately, allowing you to send huge armies of stormtroopers in at the same time from very early on. As a Rebel you’ll have to wait until HQ level 4 to build this.
If you want to play with more than one account so that you can play as the Rebels on one and the Empire on the other, then you’ll need two devices. Log one device out of Game Center or log in with a different Apple ID on the second device. You will only be able to battle against other players when they are the opposite faction that you are.
You will also only be able to join a Squad when they are the same faction as you are. If you want to reset your squad you’ll have to delete your app, then reinstall and overwrite it, at least until the developers add a way for different factions to form one squad together. So if you want to do the Clash of Clans thing and form a squad with your coworkers or buddies, you’ll have to sync up your factions first before you can invite everybody to join.