Tanky.. please read before downvoting..
Its the way i go eve jungle. 21/9. You rush trinity. Then start building tanky, getting GA fast. Ad eve damage is capped and ap eve is hindered.late game with oracles and how.shes squishy. This is specifically for gankin a lot. People willtarget you because your eve. But now itll take longer for them to kill you aka your adc amd top (hopefully more damage than tank) and.mid have more time to hit them. If someone is getting away, her kit specialized on sticking to enemies, allowing you to chase. This is fairly hard to achieve since you go from ad damage to hybric tanky. But it is a destraction mainly. How often have you seen a tanky eve? How fast does eve usually die? Her q allows her to hit mulitple targets fast. Aim her. Now you dont die so fast. Andbecause of eves passive, you can give blue buff fairly early without suffering too much

AP Mid Eve is ridiculously strong. Her Q and Ult scale off of AP. DFG + Guise + Abyssal is just really strong.

She has an AS steroid, abilities scaling to AD, and an extremely potent stick, plus her ult. If anything, her kit implies she can be built any way you want. And people built her AD viably long before anyone though of AP in the current seasons.

You're not making a compelling argument for why she shouldn't be built AD. You seem to be mixing up soaks with assassins, but that's another can of worms.

Banking on your opponent's team being stupid is a bad idea.

Not that you want to ignore survivability on Eve, but more so that it's not your job to be absorbing blows, especially when you build AD centric. Eve's got some of the best clean up potential for a reason, and emphasizing gear that keeps you alive too much throws that out the window. Trinity Force and a GA is about all you need.

And eve fundamentally doesn't need blue buff. Her abilities are on low CD's, and her mana problems are virtually non-existent.

AP mid is a popular build, but because of that people know how to counter it. If it remains popular, it'll get nerfed, and if it doesn't you'll find yourself facing Ryze or Katarina every single game.

Ap, but that's because of liandry's... if you are jungling though, I still upvote madreds (just don't finish it)

with all these responses, its pretty clear that the true answer is both, there is no right way to play a champion, you just gotta build her to your play style.

with evelynn, her best chances are playing her in 2 different styles, either a sustain fighter, or a guerrilla tactics.

lets go through her abilities, hate spikes will have no difference between if you went ad or ap, the ratios are exactly the same. and dark frenzy wont have any affect on either ap or ad as well since its a movement speed steroid and has no ratios.

the only ability that will be affected is ravage, the ratios on this ability is that ap is 10% higher than ad thus the burst potential is higher with AP, but because it also activates an attack speed steroid, AD will gain benefits to dish out more damage quickly after ravage has hit.

with her ultimate. you will only get an AP ratio making the burst potential high with an AP style champion, but for an AD champion, you'll be slowing the target and given a shield which would means you can dive in and stick to your target dealing massive damage.

so if you go pure AP, i'd suggest playing her as a hit and run, go in and dance around them while you hate spike poke them till they're low and then jump in and burst them down.

if you go pure AD, build a little tankier with resistance and you can duel your opponent to the death.

though if you go a hybrid with both hextec gunblade and guinsoo's rage blade, you'll find yourself having the best of both worlds while also gaining great sustain through the multiple vamps

so dont decide how to play her just because what someone says, play her how you like to play her, just build her properly based on that.

Ap shes amazing

Never build eve straight AD, she's outclassed is that area.

Mixed eve is viable in the jungle, she has good mobility and strong ganks.

AP eve is also a viable jungler, she has less sustain that mixed eve, though.

AP eve mid has good sustain, decent farming potential, and roams incredibly well.

personally I like ad eve more.
core build is boots, trinity, ga, mr item (qss sword/wits) I usually throw in primary damage item. Usually is just the jungler ad item for a bit more damage.
I like ad eve specially with the constant nerfing of ap because she has a lot more survivability, her burst isnt nearly as good but it makes her amazing at backdooring, and sustaining fights.
With the bit more tanky and w you can pretty much escape most fights alive.
I play her in the jungle of course. I have played ap jungle too. Usually i just pick ad or ap based on the rest of teams picks.
I do love eve jungle, its not as strong as s2, but with the increased number of wards with sightstone her stealth is strong for ganks.

Ad > AP imo
build her more like a bruiser though