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In Xenophon's Anabasis I ran into the following part:

The Persian bows are also large, and consequently the Cretans could make good use of all the arrows that fell into their hands; in fact, they were continually using the enemy's arrows, and practised themselves in long-range work by shooting them into the air. In the villages, furthermore, the Greeks found gut in abundance and lead for the use of their slingers.

Xen. Anab. 3.4.17

Translation by "Xenophon in Seven Volumes, 3. Carleton L. Brownson. Harvard University Press, Cambridge, MA; William Heinemann, Ltd., London. 1922."

Xenophon points to the fact that the Cretans used arrows taken from their Persian foes all the time (διατελέω in Greek) and even started training to use them more efficiently.

The question: were the ancient Persian arrows that superior so the Cretan archers started using them exclusively and trained for them?

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    Interesting question. That "also" in the first sentence leads me to believe some context has been omitted here though. My suspicion would be its text pointing out that their bows and arrows were similar to the Cretans', and thus this is only pointing out that they used mostly compatible ammo (and presumably that may have worked both ways). – T.E.D. Feb 22 '18 at 19:46
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    Well noted indeed. The "also" in the text is a somewhat controversial piece of text. In the translation a note was made about it being unclear as to what it connects to: perseus.tufts.edu/hopper/… – The Sardaukar Knight Feb 22 '18 at 20:07
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    Very interesting. Since they didn't write it down, its tempting to think this refers to some off-color unwritten cultural meme about Persian anatomy ... – T.E.D. Feb 22 '18 at 20:23
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A slightly different translation reads as follows:

The Persian bows were also large, so that such of their arrows as were taken were useful to the Cretans, and they continued using their enemies’ arrows; and they practiced shooting them upward, sending them a long way. They found a lot of gut in the villages, and lead, which they could put to use for the slings.
(From Wayne Ambler: "Xenophon. The Anabasis of Cyrus", Cornell University Press: Ithaca, London, 2011.)

A note on the Greek διατελέω: bring quite to an end, complete, finish, as a journey or road, […], with the end in view, complete the march, finish the distance, continue to do, or do constantly (the participle containing the leading idea.)
Putting on my speculative literary interpreter hat this opens up some interesting possibilities. Shooting Persians with Persian ammo completes the destiny of the ammo?

Seriously:
The enemy arrows were compatible and suitable for Greek uses. That is an immense advantage if you are in enemy territory, far away from your own re-supply.

From Xenophon you can not conclude that these arrows were superior, but that the Greeks used scavenging tactics to recycle them for the next battle.

The Cyreans carried some things because they had to, other things because they wanted to. They carried the tools of their trades – shields and spears, sling bullets, arrows, javelins. They carried the necessities of life – food, water, firewood, cooking pots, cloaks, tents. They carried plunder, anything that looked portable and valuable enough to haul over one hill after another. The things they carried were as heavy and unwieldy as hammered bronze breastplates, as light and tiny as flint and tinder. Only a few had animals or slaves to help with the carrying.
Examining what the mercenaries carried significantly enhances our appreciation of the arduousness of the march. The Cyreans shouldered not the light, waterproof synthetics we take for granted, but bronze, leather, wood, and wool. Their non-combat gear was not standardized military-grade, but a me ́lange of borrowed and adapted items neither designed nor built for years of continuous hard use. More importantly, understanding the characteristics and sources of Cyrean equipment is essential to assessing the troops’ behavior. Reliance on suskenoi, reluctance to abandon equipment, vociferous protection of pack animals – all make more sense when placed against the practical context of the army’s gear.
Archers and slingers could carry an additional quiver of arrows or sack of bullets with less difficulty, but they too are unlikely to have lugged huge quantities of extra ammunition. For all three light infantry types, then, a total missile load of about 3 kg (6.6 lb) seems reasonable.
The Cretan archers certainly found ways to keep their bows in action, perhaps even fashioning arrows en route using foraged reeds and fletching.
Probably some Cyreans had the skills, but they could not carry hammer and anvil along on the march. So damaged metal items must have remained in use as long as possible, being discarded only when completely unserviceable. The best craftsmen in the world, though, could not keep the Cyreans in fighting trim through repairs alone.

And most relevant to your question:

Because Persian and Cretan bows were of similar design, the Cretan archers were able to collect and reuse Persian arrows. In some cases, captured ammunition found creative reuse. The peltasts, for example, converted oversize Carduchian arrows into javelins, fitting them with thongs for greater throwing force. (p130)

The reason why they practised with them "by shooting into the air", or "shooting them upward, sending them a long way" instead of target practice, is that an arrow that has hit something is often damaged and thus non-recyclable.

Xenophon himself lost his shield in battle, and he was not the only one.139 Light troops had other problems. Discharged arrows and sling bullets were usually impossible to recycle. Javelins were perhaps easier to recover, if their slender shafts did not break. […] At greater distances, though, the penetrating power and lethality of arrows and javelins dropped markedly.

Another reason for the "practice of shooting long" is mentioned slightly earlier in the text, Xen. Anab. 3.3.15:

Now the enemy shoot their arrows and use their slings from such a distance that the Cretans are not able to reach in response, nor are those who throw by hand able to reach them.

While the Greek archers were not bad or ineffective (The Place of Archery in Greek Warfare), in comparison with their Persian counterparts, there was a bit left to be desired.

Moving from exegesis of Xenophon to the more general question of Persian arrows, it is not so much the ammunition that counts in this respect but the launch system. This system consists of the bows, archers, and tactics on the battlefield.

The Persian archers were among the finest of their time and neither these tactics nor the sheer numbers can be dismissed:

Though equipped and trained to conduct shock action (hand-to-hand combat with spears, axes and swords), this was a secondary capability and the Persians preferred to maintain their distance from the enemy in order to defeat him with superior missile-power. The bow was the preferred missile-weapon of the Persians. At maximum rate of fire a sparabara haivarabam of 10,000 men could launch approximately 100,000 arrows in a single minute and maintain this rate for a number of minutes. Typically the Persian cavalry would open the battle by harassing the enemy with hit and run attacks – shooting arrows and throwing small javelins - while the Persian sparabara formed up their battle-array. Then the Persian cavalry would move aside and attempt to harass the flanks of the enemy. Defending against the Persian cavalry required the enemy infantry to congregate in dense static formations, which were ideal targets for the Persian archers. Even heavily armoured infantry like the Greek hoplites would suffer heavy casualties in such conditions. Enemy infantry formations that scattered to reduce casualties from the dense volleys of Persian arrows, were exposed to a close-in shock assault by the Persian cavalry. Torn by the dilemma between exposure to a gradual attrition by the arrows or to being overwhelmed by a cavalry charge on their flanks, most armies faced by the Persians succumbed.

As we know, this passage seems to overstate the effectiveness of the Persian army against Greek armour or tactics in only slightly later times than Xenophon describes.

A Greek hoplite could quite happily rely upon his bronze helmet to keep out both Persian and Scythian arrows, and on his breastplate and greaves, if he wore them. On the other hand, his armour was far from complete, and the eyes, right arm, and the neck were particularly vulnerable. His shield would provide adequate protection against arrows from the Scythian bow…, but not, at short range, against those from the Persian infantry bow.
(From: P. H. Blythe: "The Effectiveness of Greek Armour Against Arrows in the Persian War (490–479 BC)", PhD, University of Reading, 1977.)

But the numbers illustrate just as nicely as

"Because of the arrows of the barbarians it is impossible to see the sun", Leonidas replied, "Won't it be nice, then, if we shall have shade in which to fight them?"

how much re-supply for ammunitions was available on a typical battlefield in the aftermath.

Source: John W. I. Lee: "A Greek Army on the March. Soldiers and Survival in Xenophon’s Anabasis", Cambridge University Press: Cambridge, New York, 2008.

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    This covers my question nicely. Let's give others the chance to respond as well, but this seems like a great accepted answer. – The Sardaukar Knight Feb 22 '18 at 20:10
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    Re: "The reason why they practised with them 'by shooting into the air', instead of target practice, is that an arrow that has hit something is often damaged and thus non-recyclable": I don't get it: even if you shoot into the air, it will still end up hitting something (such as the ground). Why does that less damaging than hitting a target? – ruakh Feb 22 '18 at 22:02
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    @ruakh Hitting a target, especially a hard one, in 50m has more energy on impact than an arrow that flies further, just falling down on landing. Admittedly, not a perfect method, but to an extent less damaging. – LаngLаngС Feb 22 '18 at 22:07
  • @LangLangC Do you have any references or math showing that there's more energy in the direct shot versus the high shot? Absent an atmosphere, the high shot should have (very slightly) more energy upon impacting the ground that the direct shot would have upon impacting a target a meter above the ground. But, we have an atmosphere, as did, I believe, the ancient Greeks and Persians and all the references I found with some quick searching simply stated that air resistance would be a factor, but neglected to indicate how much of an effect it has. – 8bittree Feb 22 '18 at 22:39
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    @8bittree I added a reference, but do not have exact numbers on energy. From personal shooting experience: Perhaps it becomes more obvious if you also consider the angle. If it is so steep that gravity becomes a significant factor it will be different compared to a much lower trajectory that results in drag petering out the energy while not much distance to fall down? – LаngLаngС Feb 22 '18 at 22:45

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