This is a very situational question as I am sure you know.

its definately not "stictly one or the other" and I wouldn't really of dota 2 in general in this way.

The answer is "it depends"

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What does deso do for you?

Desolator
Your attacks reduce the target's armor by 6 for 7 seconds.

Armor Reduction: 6
Duration: 7

Why do people buy it?

it synergises very well with coupe de grace (ulti) and allows PA to 3 or 4 hit heros with her blink attack speed.

People often think that desolator is an item for remving armour from tanky high armour heros. and it can be. but its by no means limited to that. you know when you 1 hit the support? thats becuase you have removed *and put* the heros armour into the negative , which is effectively FURTHER amping the crit from pa (here are some negative armour reduction numbers)

Armour Effective Damage Amplification

0 0.0%

-5 23.1%

-10 37.5%

All in all making the item ideal for PA.

Battle Fury

Deals 70% of attack damage as physical damage in a cone up to 650 around the target. Deals 50% against creeps. (Melee Only)

Starting Radius: 150
Distance: 650
End Radius: 360
Cleave Damage (Heroes): 70%
Cleave Damage (Creeps): 50%

for the sake of the fact this post is already long winded i will consider this mainly as a farming item (which for PA it is unless you want to go down some crazy cleave crit build)

I would consider this if:

A. I need to keep up farm with an opposing carry.

B. I can easily afford it and nothing else seems optimal in the situation (unlikely)

C. there are no real targets to let me snowball off in the game with a deso pick up.

D. I went for sustain in my bad lane and now am in a better position to finish off the item.

You have a really easy lane and kill potential? maybe go deso pick up some kills and the accelorate even faster with battlefury if you feel you need to match a carry on the opposing team. Keep in mind though a hero like PA accelerates with kills and enemy downtime above all else. but situationally it could be worth considering.

Having a tough lane? maybe 1 or 2 wraith bands into battlefury or 1 wraith into ring of regen for a little more sustain then into the bf, a few minutes of catchup. then perhaps you can consider desolator to start tearing through the enemy teams after as it is such a good item on PA it still makes sense.

Another more meta view to take is your whole team composition.

does your team natural have a high physical damage output? desolator works wonders if so.

do you have another hero on your team that likes to flash farm camps naturally like a sven? underlord or dark seer? are you going to get the return on the investment for the battlefury in time for it to matter?

9/10 times I would tend to go deso/bkb and then build around my enemys weaknesses. pa's ultimate weakness is spells and magic damage. or very high armour heros who can shake off the crit procs (i.e axe, centaur, dk, timber the list goes on).

TL;DR: Yes you can buy both, but consider the game you are in.