Hi Qryzag,
Just going to put in my two cents here...some of what I say will probably align with others. And in this discussion, note that my comments are specifically about building in Arena or other non-Conquest modes.
I do want to clarify that I don't specifically say not to use/buy crit items in the guide (at least to my recollection). In fact, I do list Fail-Not as a functional item (due to its ability to crit-debuff an enemy for your teammates to take advantage).
The main points why you might choose crits or Qin's routes for basic attackers often have to do with the god in question, as well as the enemy comp. For hunters, either route can be okay, but it's often best IMO to go crits when you use a god with an attack speed steroid, like Art or Rama. This allows you to build a bit less into attack speed items, and concentrate on power and pen (since crits scale from your power/basic attack damage). This isn't to say that crits can't have both...Wind Demon and Poisoned Star obviously have AS. I do feel PS is on the weaker side right now, and its passive really makes it less suitable for a teamfight mode.
Cost and Power Curve: But some of the items that work best with crit builds are more expensive. Deathbringer is the most expensive item in the game, Fail-Not isn't cheap, and you'll often see it alongside other items such as Bloodforge (expensive), Wind Demon (moderate), etc. In a shorter mode like Arena, getting your build online as soon as possible is important...you've got a limited time, and being able to optimize your damage potential ASAP is key. Of course, if you get a lot of early kills, you can build more quickly. But note also as Kriega pointed out that crit builds don't really become more effective until you've built at least ~50% crit chance...and that means your build doesn't really come online until like, item 4/5. (And no, you don't want to get WD 2nd and DB 3rd or 4th...your build list doesn't even include
Negatives about crits: Crits, can be partially countered by things such as Geb (passive), Hide of the Nemean Lion, Spectral Armor, and Shield of Thorns. It also relies on RNG (random number generation), which means it's a roll of the dice as to when you get a crit. This isn't a big deal if you're building more than, like, 70%, but sometimes the dice won't roll your way and you'll get 3 hits in a row without crits, for example. Makes it slightly unreliable.
Qin's, on the other hand, focuses more on attack speed to take advantage of the item's passive damage bonus. The more often you hit, the more bonus damage you get. A lot of the items that pair well with Qin's in a high AS build are cheaper...things like Odysseus' Bow, for example, and the O-Bow passive is also functional for teamfights. And of course, you're talking about consistent damage...no random chances here.
Qin's, in addition, is great against tanks that build high health. Often as a hunter, you're going to be in the backline, and your main contact is going to be against their frontline (usually tanks).
One final thing is with regard to Assassins rather than Hunters (since I don't know if you're talking about a specific class). Depending on the assassin, they'll have a stronger function with one or the other. Mercury can crit with his 1. Serqet can crit (up to 3 times) with her 1. Ne Zha has crit activation in his 2, and has (essentially guaranteed) crits in his ult, which makes Deathbringer quite nice. Most other assassins won't build crits.
But some are basic attackers, and those usually want Qin's over crits. Why? In the case of Arachne and Kali, for example, both have quick attack progressions (where at least one of their hits is faster but deals less damage). In those cases, you'll get more Qin's procs in the same amount of time...but if you were to crit on a shorter attack, you'd get reduced damage multipliers and thus lower potential damage. And while Bakasura doesn't have a variable attack progression, his Butcher Blades wants to hit as often as possible, so you want to build high AS, and this goes hand-in-hand with what Qin's wants.
In the end, as I said at the beginning, most of my build direction preference depends on enemy comp and the god I'm using.