Different armour enchantments stack.
As long as they occupy different slots, yes. You cannot, for example, have a +1 Leather Armor of Stealth +5 underneath a +1 Full Plate of Fortification. Whichever one you occupied last will suppress whichever one is covered. For some reason.
This leads to some interesting ramifications in some cases. It's possible to wear a whole slew of Anklets of Translocation in 3.5, for example, each of them giving Teleport 10f.t. as Swift Action 2/day. But you'll have to take one of them off for each two uses, so you can use the next anklet.
It also begs the question why you can have 1 anklet, but it suppresses the magic of both your shoes, since Anklets of Translocation occupy the Boot slot.
However, I am talking about the enhancement bonus to AC. That shouldn't stack. You shouldn't have +3 on one and +1 on the other and pick the best of enhancement and base AC and mix them.
Exactly, and like I said, that is why it'd be a "waste" with that +1 Enhancement on either the Bracers or the Armor, because to take other magic, the equipment in question needs to also have a minimum of +1 Enhancement (in effect "be magical" to begin with), but it doesn't stack, meaning that at least one enhancement's worth is basically thrown away no matter what you do, if you're using both an Armor and Bracers of Armor as a base for magic.
So, for example, I have Bracers of Armour 2 with enhancement bonus of +5 and +5 to Hide and Heavy Fortification. Then I have a plate armour +1 with +10 to Move Silent. If you wear them both, you do get the +5 to Hide, +10 to Move Silent and Heavy Fort. However, what is your AC bonus from the armours? I contend that it is the better of the two as discrete armours (i.e., +7 for the Bracer and +9 for the plate armour) which means you get +9. I do not believe you should get +13 (plate armour base +5 enhancement from bracers enchantment). That is where the sticky part is.
Assuming you mean "Full Plate Armor" (there is no "Plate Armor", just Breastplate, Half-Plate, etc.), in 3.5 and PF, you'd have an Armor Bonus of +9 to AC from the Full Plate Armor, you'd have an Enhancement Armor Bonus to AC of +5 from the Bracers of Armor, you'd have Heavy Fortification from the Bracers of Armor, you'd have a Hide +5 Competence Bonus from the Bracers of Armor, you'd have a +10 Move Silently Competence Bonus from the Full Plate Armor.
You would not get the Armor Bonus of the Bracers of Armor 2, because the Armor Bonus of +2 from the Bracers would be superseded by Armor Bonus of +9 from the Full Plate Armor.
You would not get the +1 Enhancement Armor Bonus to AC from the Full Plate Armor, because the Enhancement Armor Bonus to AC of +1 would be superseded by the Enhancement Armor Bonus of +5 from the Bracers of Armor.
Also, one minor note in this: There is no "Hide" or "Move Silently" in PF, there is only Stealth. The above applies to 3.5, however. It would be identical in PF, but converting Hide and Move Silently to Stealth, you'd only get the +10 Competence Bonus to Stealth from the Full Plate Armor, superseding the +5 Competence Bonus to Stealth from the Bracers.
Bar any other modifiers (such as Size, Dexterity Modifier, Dodge, Natural Armor, etc.) you'd have a total AC of 10 (Base)+9 (Armor)+5 (Enhancement) = 24.
The IE games have it correct. Bracers of Armour gave a straight up AC. Normal armour also gave a straight up AC (chainmail is AC 5 and studded leather is AC 7, for example). They do not stack as they are the same.
So the Bracers of Defence do not, in fact, "straight up give you the AC as stated", but do indeed work just like in 3.5 in this regard.
Edit: Addendum:
Cael Stat boosting items IS enhancement but their "upgrade" path is set in stone (gold cost etc.). That's how it works for the bracers too - you can't put a +1 enhancement armor bonus on them
since they're not armor (at least if I'm correct about that - I'm pretty sure like I said but not 100%)
.
If you want to enhcant bracers of armor (with either an enhancement bonus or an equivalent armor special ability), you have to pay the costs listed under the enchantment rules for the item.
It can be argued that if they give basic armour bonus, then that can be enhanced.
No it can't, not by RAW. The prices for armor enhancements is for armor. Bracers of Armor aren't armor.
Bracers are (part of) armour, especially plate armour.
Not in D&D/PF. Bracers are a discrete piece of equipment as far as magic goes. Yeah, I'm not sure I agree with how it works all the time, because I think the idea of "armor slots" is a bit game-y, and that things should be allowed to be enchanted magically in a more free-form fashion, limited mostly by the ingenuity and the wealth of the players, but given the runaway nature of powerful magic and items in D&D, this particular aspect was semi-strictly regulated (sometimes to the point of it getting ridiculous).
For full plate, Gloves (i.e. gauntlets) would also arguably be "part of the armor", but they still count as it's own discrete piece in terms of magic. Why gloves and not pauldrons, for example? Why bracers but not leg-straps/leggings? Beats me, but that's the way it is.
Edit 2: Further addendum:
Cael Stat boosting items IS enhancement but their "upgrade" path is set in stone (gold cost etc.). That's how it works for the bracers too - you can't put a +1 enhancement armor bonus on them
since they're not armor (at least if I'm correct about that - I'm pretty sure like I said but not 100%)
.
If you want to enhcant bracers of armor (with either an enhancement bonus or an equivalent armor special ability), you have to pay the costs listed under the enchantment rules for the item.
Bracers of Armor can
explicitly be enhanced as if they were Armor, in PF. In 3.5, this is arguably implicit, but very debatable and not worth going into, really. But in PF they outright, no-nonsense, 100% raw, can have magical effects applied to them as if they are Armor, meaning that you can slap a +1 Enhancement Armor Bonus to AC on them and then go to town with all the magic armor effects you can think of, (as always) subject to DM/GM approval (so I wouldn't get my hopes up for Fortification or special materials unless you've got a
really good excuse).
I'd argue that they should also qualify as Shields, but that might almost straight-up void the value of shields entirely, if you can just slap Enhancement Shield Bonus to AC onto your bracers. But
in my head, it would make more sense, sorta like Wonder Woman's bracers. I'd probably allow it in my own games, though, provided there wasn't already someone that sorta wants to do the whole shield thing. Wouldn't be nice to take away one of the major benefits from another player and give to everyone.
Edit 3: Goddamn, I was wrong on something. You don't actually need to put a +1 Enhancement Bonus on the Bracers of Armor in order for them to have other armor special abilities. They just need to have at least a +1 Armor Bonus, which, all things considered, is a pretty funny rule to have considering that
all Bracers of Armor have at least +1 Armor Bonus.