Who runs Gunblade on AP Shaco over Nashor's Tooth and why?
As the title says
As the title says
Wait what
Do people actually build Nashors on Shaco? That seems pretty pointless to me, you might as well just build an AD item instead at that point and get more value out of it.
nashors is god awful on ap shaco. you aren't wanting to get in and auto a few times. fuck no
you wanna Q in, backstab their squishy, and gunblade+e if needed. They will almost certainly be dead.
Then you ult, hope you don't die, and q out.
GUnblade>nashors by 100000000x
Not to mention with runic echos and gunblade the proc alone is 300 dmg
I don't build gunblade because I'm not building any armor pen so even if some of his abilities have AD ratios, the damage isn't what it actually says if they have armor. Your forgetting that Q is an auto so you will have to incorporate it into the combo. If your going AP might as well do it all the way instead of with a half ass item like Gunblade to get the most out of your magic pen.
tbh you don't need armor pen even building gunblade. most of your damage is going to be magic anyway.
Qing them isn't hard due to being stealthed. Just q in and backstab the squishy>gunblade>E>smite+ignite if needed and they are almost certainly dead.
You are forgetting that gunblade comes with a 250 active and a 30% ap ratio i believe. That is absolutely massive, and way more dps than a nashors could ever hope to add in a rotation.
They have equal ap, but gunblade also has a bit of AD which is added into his damage output. Nashors tooth, the attack speed really isn't helping that much, nor is the proc. The CDR i can see being beneficial, but not enough to get it over gunblade
Idk, maybe you play shaco an entirely different way than i do. But I'm pretty sure most would agree nashors is in no way, shape, or form as good as gunblade or even close. They aren't even in the same conversation imo. You gotta be going for an entirely different build/playstyle. I don't think nashors would be good at all on a pure AP shaco
Gunblade falls off too hard for my taste on AP shaco. Especially when the enemy starts building armor and MR does it really start to feel bad. Also Nashor's tooth synergizes way more with Shaco than Gunblade. The CDR is so nice on him. The on hit from Nashor's (which scales with 30% of your AP) also works on your clone so it can really pump out damage if not killed (which no one wants to do unless from a distance). Faster clearing in general. I don't run ignite on Shaco either. If your able to cheese as Shaco in his current state and after the jungle changes, well I don't think your playing against adequate players then. Your really underestimating the damage output of Shaco when he has

i just can't imagine wanting to actually stick around to get use out of the on hit ability. I feel like if you don't burst someone down most champs can just turn around and fight you (assuming they know how to tell which is the clone and attack you)
what do you mean by cheese? do you mean instagiebing them or early gank cheese?
ganks at level 2 or invading the enemy jungler. The combo when I'm trying to pick someone off solo is Q ,W, R, Auto, E. If that doesn't kill them instantly the follow up damage definitely will. Plus you are way more useful in team fights simply by switching out Gunblade for Nashor's tooth since your clone does significant damage with autos, your boxes do more damage, and you can use your Q faster. I will admit that you don't spike as fast by taking this build but you definitely spike hard and scale better than with Gunblade.
FLASH OR DIE
IGNITE IS FOR THE WEAK
I build both a lot of the time. AS has synergies with the AD from Gunblade, and the On-Hit effect works on the clone, giving you some free damage even when they know it's the clone and have to avoid attacking it. The combo also helps waveclear and objective damage significantly.
I don't have room for gunblade in my build.

10% cdr in runes
AP shaco is built to maximize burst. Gunblade's hybrid stats benefits his new kit even better (hybrid ratio on Q and E, Q's auto still applies 100% of his AD on top of the bonus damage etc) on top of the active itself.
With
Q-Gunblade-E is very high damage all in a very short span of time
Nashor's is a DPS item and if you want DPS you're better off with AD Shaco
Its very high if they have no armor or magic resist. otherwise a lot of that AD damage is mediocre if they have armor.
this is almost ALWAYS enough to kill a squishy
Do you build the lichbane first? I prefer gunblade tbh but i havent gone with a LB first so ill give it a try
what do you build first? Movement thing im assuming?? or the sheen?
I go runic, sorc boots, lich bane (unless I get super ahead early game then I go nashers second), Nashor's tooth, void staff, and then death kap. ( I use k kouse I'm kool like that).
runic and gunblade first, the revolver+runic procs thunderlords instantly if you backstab.
very good burst
oh okay yeah i do the same, just LB beinglisted first i was like um wut
what piece of lichbane do you build first?
i always build the one that gives movement speed tbh unless i can go blasting+amp tome but not enough for anything else
after I finish gunblade I usually get sheen if I can afford it, otherwise I get the wisp
my build is usually in this order 
->
->
,
and then either
or
, then build the other last
nashors helps in farming phase with aa speed. as well as a significant ap boost when sending your decoy and Q E into a full team.