Agi or Damage?

What is more beneficial for agi hard carries, such as faceless void or spectre or weaver...

Damage or agility? all other stats aside.

Agi ofc since it gives Damage, AS and Armour.

But you have to take all other stats into account. I prefer a butterfly to say a desolator or a radience for obvious reasons

All depends on the character ;)

Well, you can look at it like this:

One Slippers of Agility grants 3 Agility for 150 gold.
One Blades of Attack grants 9 Attack Damage for 450 gold.

With the Slippers, you pay 50g per Agility. One point of Agility grants not only one point of Attack Damage, but also .14 armor and 1 attack speed.

With the Blades, you still pay 50g per Attack Damage, but for the same price, you're passing up free armor and attack speed you could have had with the agility items. It's pretty clear when you do the math that it is almost useless to build damage with Agility characters when you have options available to build raw Agility. The only reason you should grab damage instead of Agility is perhaps for inventory space or if different items are more cost effective. (Also, obviously, if the Attack Damage items build into items you want for their active/passive effects.)

Be careful, though. Some Agility items aren't as cost effective as they appear. For instance, three Slippers of Agility give 9 Agility for 450g while one Boots of Elvenskin cost the same amount and only give 6 Agility. Of course, when compared to the next tier of Attack Damage item, the Broadsword, it is more cost effective.

With the Boots of Elvenskin, you pay 75g for each point of Agility. With the Broadsword, you pay 66g for each point of damage. Though the disparity is less severe in later levels of gear, you need to take into account that 18 agility is much more effective than 18 attack damage, even if 18 agility would theoretically cost 1350g while a Broadsword with 18 ad would cost 1200g.

Faceless Void - Rush a Mask of Madness -> Standard built -> Increased attack speed so you can jungle a bit better between early - mid game if you have no one sitting you
Faceless Void - Rush a battlefury -> Alternative Route -> farms a lot quicker to push out items.

IMO for faceless void i'd like to rush a MoM to get that nice attack speed a be a little helpful in team battles if required, grabbing a mask of madness first allows you to push out your stuns out on a single target alot faster. After you farmed most of your items MoM is useless because you should of already reached cap attack speed.

For Drow Ranger i usually rush PURE AGILITY for that super fast attack and damage and the ability to kite people down along with that i ma out her third and last as fast as possible then i max out slow and at least 1 skill point into silence.

Weaver -> DAMAGE -> IMO damage because one of his skills which should be the third skill allows him to attack twice every couple of seconds which would be amazing for harassing early game and ganking.

Juggernaut -> spin/attribute -> get spin and attribute until lvl 7 so you have the mana to spin and ultimate right after each other since juggernaut doesn't carry a large mana load to do both consecutively.

I prefer to get spin/attribute/ultimate until lvl 11 then i would have enough to farm with spin/ blade storm/ and omnislash and have the HP to take incoming damage.

Don't hate these are my opinions of the game, I enjoy my playing style if you don't then don't insult just post your own comment

Another thing to keep in mind: VS and Drow's auras both only deal with the damage given by primary attributes and base damage and not the effects of BKB or Daedalus. So having those characters on your team increases the value of agility (or intelligence or strength).

Let's see, a level 1 Faceless Void with a Slippers of Agility would have 44 DPS although it does increase his EHP up to 844, having Blades of Attack would grant him him 45, at level 6 He'd have 52 DPS with Slippers and 53 with Blades, if talking about cost-effectiveness grabbing AGI items does provide near same benefits in contrast to items granting raw damage. The idea of grabbing Mask of Madness on the other hand is quite suicidal, see, a level 6 Faceless Void with a PT-MoM would have a DPS of 94, the closest to compare would be one having PT-Yasha which grants a DPS of 87, the big downside is the fact that you're lowering your EHP because of Berserk which is quite dangerous especially on situations where you fail to trap all of your enemies inside your Chronosphere.

Anyway on topic, depending on the hero's AGI gain there would be times when grabbing Raw damage would be beneficial than stacking up minimal AGI.

At the end of the day - it doesn't matter what the base item does, slippers or blades - it's what you plan to do with them after that counts. if you're just going to sell them, then you're buying them for no reason. if you plan to build into something ie crystalys or phase boots, poormans or ring of aquila then of course adjust accordingly.. you also need to consider your slots. 3 slippers take 3 slots, 1 blades of attack takes 1..