I'd recomend FE, but I've only ever had build up and realise just how situational that is for a brute
"Well, they found my diary today.
They were appropriately appalled
at the discovery of the eight victims
They're now putting it all together.
Women wrapped in silk
with one leg missing
Eight legs, one body, silk,
spider, brilliant!"
If your getting both I recommend build up since it has the ACC bonus.
well that's simple, FE is a boost for 20s on fire and 10s for letal/smash.
so you've got 200% on damage on the first 10s if you fight with fire/smash
the damage boost is really good and it got a little 40% of accuracy, that's clearly better for me than build up.
Just to Clarify then.
Fiery Embrace does NOT have an accuracy improvment
It does NOT give you 200% damage for the first 10 seconds.
You activate it and for the first 10 seconds all attacks gain 100% damage
the remaining 20 seconds only fire "based attack" get the 100% bonus.
"fire based" itn's clear wether it means fire damage or all damage if the attack has a fire element. With fiery melee thought this is pretty good.
Build up on the other hand only lasts 10 seconds, gives 100% damage and alos 60%~ acc bonus. It has only 90 second cool down (fiery embrace is 180). So really the bonus is about 2/3 that of firey embrace. Though not all damage is fire based and so we get closer to them beign equal in terms of damage. Imho build up wins since it's nearly equal on damage over time but also has that accuracy bonus. If you don't have fiery melee then build up wins hands down. I'd definatly take botyh but build up fuirst (it is a primary after all, primary generally better than secondary)
That being said, 30 secs of extra damage on a boss can be better than just 10 seconds of extra damage and acc. However, build up with recharge can usually be availibly for each group (depending how fast you kill things). Build up + blazing Aura+fire sword circle as an opener comined with high fury from the previous group leads to some wicked damage =). Can't do that everytime with FE as the cooldown is twice as long.
*edited for the sake of pedantics 
[ QUOTE ]
You activate it and for the first 10 seconds all attacks gain 100% damage
the remaining 20 seconds only fire "based attack" get the 100% bonus.
[/ QUOTE ]So it only has 100% fire all the time, not 200% for the first 10 secs?
Also, it's fury, not rage.
I thought it was 100% damage boost for 20 secs of wich the first 10 seconds all damage and the remaining 10 seconds only fire.
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[ QUOTE ]
Duration is 10 seconds for any type of attack, and 20 seconds for fire based attacks.
[/ QUOTE ] Interpret it as you will. I havn't gone and tested it or anyhting. Description is from the hero builder thing. Considering it lasts for 30 seconds I assuem the 10 second bit refers tot he first 10 secodns and the 20 second bit to the final 20 of the 30.
Just to give you a bit more of my logic, you dont want to be stopping mid group to hit your damage increase, you could be attacking and maintaining fury. FE lasts longer, thus if you use it at the start of every fight you'll get more out of it. BU doesn't last one full attack cycle for me, so the idea of hitting it mid fight and wasting that animation time is less than apealing, I mostly only use it for the acc bonus vs CoT, or for my AoEs at the start of each fight.
"Well, they found my diary today.
They were appropriately appalled
at the discovery of the eight victims
They're now putting it all together.
Women wrapped in silk
with one leg missing
Eight legs, one body, silk,
spider, brilliant!"
What Cynic said - I picked up both BU and FE (in that order), and my main use for them is as a quick self-buff before battle when Fury is zeroed. Occasionally, I'll hit them before some bosses and AVs in the middle of battle - nothing quite like 2-3 shotting a +2 Boss. 
@Synaesthetix
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Duration is 10 seconds for any type of attack, and 20 seconds for fire based attacks.
[/ QUOTE ] Interpret it as you will. I havn't gone and tested it or anyhting. Description is from the hero builder thing. Considering it lasts for 30 seconds I assuem the 10 second bit refers tot he first 10 secodns and the 20 second bit to the final 20 of the 30.
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It doesn't last 30 seconds, that was nerfed in I5 to 20s.
Your explanation is correct. All damage types are buffed in the first 10 seconds, then only fire for the next 10 seconds.
Coming up to 35 and don't know weather to get BU or FE :P I will be getting both, but since I'm fire Primary I should take FE first ?