My memory is very hazy on this so I can't be to helpful, but I think doing missions for Duty or Freedom may get you rewards like special armour you might not be able to otherwise get. Unfortunately I can't remember if any of the missions that give you those rewards require you to attack the other faction (making them hostile) or if there's a way to do it for both factions.

Something I feel like suggesting though, is either just do whatever you feel like doing rather than worrying about which gets you better gear/rewards, you'll probably have more fun just doing what you want and immersing yourself in whichever path you choose. Or follow one side so it will make it easier to see the other side should you replay at some point.