I'm in a dilema right now, I've found two pieces of enchanted Dwemer cuirass, one with Resist Normal Weapons 11% and the other with Shield 12%.

Which one is more beneficial or "better" (as in, helps me live longer in combat )?

Personally I'd go with shield since you will benefit from it against a broader number of enemies. I don't think resist normal weapon protects against animal or monster attacks (unless the monsters are wielding weapons), only against enemies wielding normal (as in not silver or enchanted or Daedric) weapons.

Shield is also a more common enchantment so you are more likely to find other pieces to boost your AR further.

Got it. Selling off that Resist Normal Weapons cuirass right now. =P

Well, there is a difference in that the Shield effect essentially boosts your armor rating, and that maxes out at 85%. Resist Normal Weapons is cumulative with armor rating, so if you have a 50 point hit coming in from a normal weapon, and you have 20% resistance to normal weapons and a 70% armor rating, then you would receive 50 x .8 x .3 = 12 points of damage, versus 15 points if the resist were not in place.

So if between armor plus shield effects, you are already at 85% then adding the resist normal weapons would still have benefit, whereas the additional shield effect would not.

Though as already mentioned, there are lots of attacks that it won't help with (silver, enchanted, daedric weapons, magic, poisons, non-weapon physical attacks) so not that valuable of an enchantment if you have other choices.