While you are fighting your active weapon (primary, 2ndary, heavy) is the one that gains xp. I'm wondering if armor gains xp by being hit/taking damage. In otherwords: if I want to level armor faster (outside of bounties) should I intentionally let myself get hit to level armor faster?
No it does not. The only way to gain experience is from finishing bounties, story missions, and the strikes.
I tested it out and you do not gain experience from taking damage. I used DestinyStatus.com to view xp before and after. I took a baseline after a couple hours idle. Then dropped into Mars patrols and killed one Cabal, by myself, without taking any damage. Took an xp snapshot. Then allowed myself to take damage from a single cabal, without dealing any damage. No experience was gained.
You won't get any XP from getting hit. Aside from completing bounties, story missions, and strikes, you can get XP by killing things and also by your people in your fireteam killing things. Trust me. I've played a lot of Destiny.
My favorite way to level gear and weapons is to complete bounties and then make sure you have the stuff you want to level up equipped when you turn in the bounty. Also, if you do a public event you get a package in the mail (Once per day). When you pick up that package you get a bunch of XP so equip your gear that you want to level when you pick that pack up from the postmaster too.
You can complete most of Eris' bounties just by going to the moon and doing The Dark Beyond mission farming method. Check out this video here to learn more about that:
Actually, these responses are all wrong. I know for a fact that taking damage WILL level up your armor... I was a short way from obtaining a new upgrade for one of my armor pieces and wanted to try this technique so I started up a strike and didn't shoot my weapon or melee anyone. I let the other guys kill. I just ran around and took damage and sure enough, upgrade UNLOCKED!!!... since then, I have tried this technique many times, just taking as much damage as I could and by the end of the strike you will end up with WAY more xp for your armor. I have also compared this to strikes where I killed everything that moved and took very little damage...and not nearly the same amount of xp was gained....so YES...your armor DOES upgrade by taking damage... NOT from kills.